Introduction to Physics FAQ

This FAQ provides answers to frequently asked questions about the Introduction to Physics course. Questions are organized by category and difficulty level to help you find the information you need quickly.

Getting Started Questions

What is this course about?

This is a comprehensive year-long high school physics course that develops scientific literacy through systematic progression from foundational knowledge to creative application. The course covers 200+ physics concepts organized into 12 major areas: Foundation, Kinematics, Dynamics, Energy, Momentum, Rotation, Oscillations, Waves, Sound, Light, Optics, and Electricity. The curriculum is structured using Bloom's Taxonomy (2001), taking you from remembering basic principles to designing original experiments and solving real-world problems. You'll engage in hands-on laboratory work and interactive simulations (MicroSims) that make abstract concepts concrete and keep learning engaging.

See: Course Description

Who is this course for?

This course is designed for high school students in grades 10-12 who have completed Algebra II and Geometry. It's perfect for students interested in STEM fields, those preparing for AP Physics, students considering engineering or science careers, or anyone curious about how the physical world works. The course challenges you intellectually while providing scaffolding and support to ensure success regardless of your prior physics experience.

See: Course Description

What are the prerequisites for this course?

You need to have successfully completed Algebra II and Geometry before taking this course. These mathematics courses provide the foundation for understanding physics concepts, working with equations, and solving problems. Specifically, you'll use algebraic manipulation, equation solving, graphing functions, trigonometric functions (sine, cosine, tangent), and geometric relationships. No prior physics knowledge is required—we start from the beginning and build up systematically.

See: Course Description

How long does it take to complete this course?

This is a full-year course designed to be completed over approximately 36 weeks (one academic school year). Each of the 12 chapters typically requires 2-4 weeks to complete, including lectures, laboratory work, problem sets, and assessments. Students should expect to spend 5-7 hours per week on coursework, including class time, homework, lab reports, and study. The pace can be adjusted based on individual learning needs and prior background.

How is this textbook structured?

The textbook is organized into 12 chapters that follow a logical progression through physics topics. It begins with Scientific Foundations (Chapter 1) establishing measurement and mathematical tools, then progresses through Motion (Chapters 2-3), Forces (Chapters 4-5), Energy and Momentum (Chapters 6-7), Rotation and Oscillations (Chapters 8-9), Waves and Sound (Chapter 10), Light and Optics (Chapter 11), and Electricity (Chapter 12). Each chapter includes concept summaries, detailed explanations, worked examples, interactive MicroSims, practice problems, and links to the learning graph showing concept dependencies.

See: Chapters Overview

What is a learning graph and how do I use it?

A learning graph is a visual map showing how concepts connect and build upon each other. Each concept appears as a node, and arrows show prerequisite relationships—if concept A points to concept B, you should understand A before studying B. The learning graph helps you navigate your learning path, identify prerequisites for challenging topics, review foundational concepts when stuck, and see the big picture of how everything connects. You can explore the interactive learning graph viewer to search concepts, filter by category, and trace dependency paths.

See: Learning Graph Introduction and Interactive Viewer

What are MicroSims?

MicroSims are interactive educational simulations embedded throughout the textbook that let you explore physics concepts hands-on. Each MicroSim allows you to manipulate variables, observe outcomes, and develop intuition about physical relationships. For example, the projectile motion simulator lets you adjust launch angle and velocity to see how trajectory changes, while the wave interference simulator shows how waves combine. MicroSims transform passive reading into active learning, making abstract concepts concrete and memorable.

See: List of MicroSims

How should I approach difficult concepts?

When you encounter a challenging concept, follow this systematic approach: First, check the learning graph to identify and review prerequisites you might be missing. Second, read the glossary definition for precise terminology understanding. Third, work through provided examples step-by-step before attempting problems. Fourth, use MicroSims to visualize and manipulate the concept interactively. Fifth, practice with progressively harder problems, starting with worked examples. If still struggling, review related concepts in earlier chapters, work with study partners to discuss ideas, or seek help from your instructor with specific questions prepared.

What is Bloom's Taxonomy and why does it matter?

Bloom's Taxonomy is a framework for categorizing learning objectives into six cognitive levels: Remembering (recalling facts), Understanding (explaining concepts), Applying (using knowledge in new situations), Analyzing (drawing connections), Evaluating (making judgments), and Creating (producing original work). This course uses Bloom's Taxonomy to ensure you develop all levels of thinking, not just memorization. Assessments are distributed across these levels, with 10% Remembering, 15% Understanding, 30% Applying, 20% Analyzing, 15% Evaluating, and 10% Creating. This means you'll spend significant time solving problems, analyzing data, and designing experiments—not just recalling definitions.

See: Course Description

How do I navigate the textbook website?

The website navigation menu on the left shows all major sections. Start with the Course Description to understand scope and expectations. Access individual chapters through the Chapters menu in order. Explore MicroSims through the MicroSims menu for hands-on learning. Use the Learning Graph section to visualize concept dependencies and explore the interactive viewer. Reference the Glossary for terminology definitions. Check the FAQ (this page) for common questions. Each chapter includes internal navigation links, prerequisite indicators, concept lists, and next/previous chapter buttons at the bottom.

What technology do I need for this course?

You need a computer or tablet with internet access to view the online textbook and MicroSims. MicroSims run in any modern web browser (Chrome, Firefox, Safari, Edge) with JavaScript enabled—no additional software installation required. For laboratory work, your school provides necessary equipment (sensors, measuring devices). A scientific calculator is essential for problem-solving, though graphing calculator or calculator app works fine. For optimal experience, a screen size of at least 10 inches is recommended, and a stable internet connection helps with interactive content.

How are assessments structured in this course?

Assessments are distributed across Bloom's Taxonomy levels to evaluate comprehensive understanding. Weekly vocabulary quizzes test Remembering (10% of grade). Concept maps and exit tickets assess Understanding (15%). Problem sets and lab procedures evaluate Applying skills (30%). Lab analysis and data evaluation measure Analyzing ability (20%). Peer review and critique essays test Evaluating skills (15%). Projects and design challenges assess Creating capacity (10%). This structure ensures you demonstrate mastery at all cognitive levels, not just recall, preparing you for advanced physics courses and real-world problem-solving.

See: Course Description

Core Concept Questions

What is the scientific method?

The scientific method is a systematic approach to investigating phenomena through observation, hypothesis formation, experimentation, and analysis. It typically follows these steps: (1) Observe a phenomenon or identify a question, (2) Research existing knowledge, (3) Form a hypothesis (testable prediction), (4) Design and conduct experiments, (5) Collect and analyze data, (6) Draw conclusions, and (7) Communicate results. The scientific method ensures investigations are objective, reproducible, and lead to reliable knowledge. It's not always linear—scientists often cycle back through steps as new evidence emerges. Understanding the scientific method helps you think like a physicist and conduct meaningful investigations.

Example: Testing whether fertilizer increases plant growth involves controlled experiments comparing treated and untreated groups, measuring growth systematically, analyzing data statistically, and drawing evidence-based conclusions.

See: Chapter 1

What is the difference between distance and displacement?

Distance is a scalar quantity representing the total length of path traveled, regardless of direction—it only has magnitude. Displacement is a vector quantity representing the straight-line distance and direction from initial position to final position—it has both magnitude and direction. Distance is always positive or zero and accumulates along any path. Displacement can be positive, negative, or zero and depends only on start and end points. For example, running around a 400-meter track covers 400 meters of distance but results in zero displacement if you return to the start. Understanding this distinction is crucial for kinematics problems.

Example: Walking 3 blocks east, then 4 blocks north results in 7 blocks total distance but only 5 blocks displacement in the northeast direction.

See: Glossary - Distance and Glossary - Displacement

What is the difference between speed and velocity?

Speed is a scalar quantity representing the rate of distance covered per unit time—it has only magnitude and is always positive or zero. Velocity is a vector quantity representing the rate of displacement change with respect to time—it has both magnitude and direction and can be positive, negative, or zero depending on chosen coordinate system. A car's speedometer shows speed (60 mph) without indicating direction. Velocity includes direction (60 mph north). Objects can have constant speed but changing velocity if direction changes, as in circular motion.

Example: A car traveling 60 mph north has speed of 60 mph and velocity of 60 mph north. If it turns to travel 60 mph east, speed remains constant but velocity changed direction.

See: Glossary - Speed and Glossary - Velocity

What is acceleration?

Acceleration is the rate of change of velocity with respect to time, measured in meters per second squared (m/s²). Since velocity is a vector, acceleration is also a vector—it has magnitude and direction. Acceleration occurs whenever velocity changes in magnitude (speeding up or slowing down) or direction (turning), or both. Positive acceleration means velocity increases in the positive direction; negative acceleration (deceleration) means velocity decreases or increases in the negative direction. Constant acceleration means velocity changes by the same amount each second, which is the basis for kinematic equations.

Example: When a car speeds up from rest to 60 mph, it experiences positive acceleration. When braking, it experiences negative acceleration (deceleration). When turning at constant speed, it still accelerates because velocity direction changes.

See: Glossary - Acceleration and Chapter 2 - Acceleration

What are vectors and how do they differ from scalars?

Vectors are physical quantities characterized by both magnitude and direction, represented by arrows. Examples include displacement, velocity, force, and momentum. To fully specify a vector, you must state both how much (magnitude) and which way (direction). Scalars are physical quantities characterized completely by magnitude alone, without directional component. Examples include mass, temperature, speed, and energy. Mathematical operations differ: vectors add using head-to-tail method or component addition, while scalars add arithmetically. Understanding vector vs. scalar nature is essential for correctly solving physics problems.

Example: Force is a vector—pushing with 50 N east is different from 50 N north. Temperature is a scalar—25°C needs no direction specification.

See: Glossary - Vectors and Glossary - Scalars

What is Newton's First Law?

Newton's First Law (Law of Inertia) states that an object maintains constant velocity (including rest) unless acted upon by a net external force. This means objects at rest stay at rest, and objects in motion continue at constant velocity in a straight line, unless forces cause changes. The law introduces inertia—the tendency of objects to resist changes in motion, proportional to mass. Newton's First Law defines what we mean by zero net force: it's the condition producing no acceleration. It seems counterintuitive because everyday objects slow down due to friction, but in frictionless environments (like space), objects truly coast forever.

Example: A hockey puck sliding on frictionless ice continues moving at constant velocity indefinitely without additional pushes, demonstrating Newton's First Law.

See: Glossary - Newton's First Law and Chapter 4 - Newton's Laws

What is Newton's Second Law?

Newton's Second Law states that net force equals mass times acceleration, expressed as F_net = ma. This quantifies how forces cause acceleration: larger forces produce greater acceleration, while larger masses produce smaller acceleration for the same force. The law is vector equation—force and acceleration point in the same direction. It applies to any object or system where you can identify all forces acting. Newton's Second Law is the most frequently used physics equation, applicable to everything from falling apples to rocket launches. Understanding this relationship is fundamental to solving dynamics problems.

Example: Applying 20 N to a 5 kg object produces 4 m/s² acceleration in the force's direction (a = F/m = 20/5 = 4).

See: Glossary - Newton's Second Law and Chapter 4 - Newton's Second Law

What is Newton's Third Law?

Newton's Third Law states that forces always occur in equal-magnitude, opposite-direction pairs acting on different objects. When object A exerts force on object B, object B simultaneously exerts equal and opposite force on object A. These are called action-reaction pairs. Crucially, the two forces act on different objects, so they don't cancel—they affect each object's motion separately. Newton's Third Law explains how walking works (you push back on ground, ground pushes you forward), how rockets accelerate (expelling gas backward creates forward thrust), and why all interactions are mutual.

Example: A rocket expels gas downward (action), while gas pushes rocket upward (reaction) with equal force, accelerating the rocket upward.

See: Glossary - Newton's Third Law and Glossary - Action-Reaction Pairs

What is force?

Force is a vector quantity representing an interaction that causes or tends to cause a change in an object's motion. Forces have both magnitude (measured in newtons) and direction. Forces can be contact forces (friction, tension, normal force) that require physical touching, or field forces (gravity, electric, magnetic) that act at a distance. Net force is the vector sum of all forces acting on an object, which determines acceleration according to Newton's Second Law. Understanding forces and how to identify them through free-body diagrams is essential for analyzing motion in dynamics problems.

Example: Pushing a shopping cart with 50 newtons of force causes it to accelerate in the direction of the push, according to F = ma.

See: Glossary - Force and Chapter 4 - Forces

What is work?

Work is the energy transfer accomplished by a force acting through a displacement, equal to force times parallel displacement (W = Fd cos θ, where θ is angle between force and displacement). Work is a scalar quantity measured in joules. Positive work adds energy to a system; negative work removes energy. Only force components parallel to displacement do work—perpendicular components do no work. Understanding work is fundamental to energy analysis, as it connects forces (causing motion) to energy changes (resulting from motion). Work provides an alternative to force-based analysis for solving mechanics problems.

Example: Lifting a 10 kg box 2 meters high requires 196 joules of work against gravity (W = mgh = 10 × 9.8 × 2 = 196 J).

See: Glossary - Work and Chapter 6 - Work and Energy

What is energy?

Energy is the capacity to do work or cause change. It exists in multiple forms: kinetic energy (energy of motion), potential energy (stored energy due to position or configuration), thermal energy, chemical energy, nuclear energy, and electromagnetic energy. The total energy in an isolated system remains constant (Conservation of Energy), though it transforms between forms. Energy is scalar quantity measured in joules. Understanding energy provides powerful problem-solving approach—instead of tracking forces and accelerations throughout motion, you can compare initial and final energy states. Energy concepts underlie all of physics and connect to everyday experiences.

Example: A roller coaster at a hill's top has maximum potential energy; at the bottom, this transforms to maximum kinetic energy, with total mechanical energy constant (ignoring friction).

See: Chapter 6 - Energy

What is kinetic energy?

Kinetic energy is energy possessed by an object due to its motion, equal to (1/2)mv² where m is mass and v is velocity. It's a scalar quantity (always positive) measured in joules. Kinetic energy depends quadratically on velocity—doubling velocity quadruples kinetic energy. This explains why high-speed crashes are so much more dangerous than low-speed ones. The Work-Energy Theorem states that net work done on an object equals its change in kinetic energy, providing an alternative to Newton's Second Law for solving problems. Kinetic energy is one component of mechanical energy (kinetic plus potential).

Example: A 1000 kg car traveling at 20 m/s has 200,000 joules of kinetic energy (KE = ½ × 1000 × 20² = 200,000 J) that must be dissipated to stop.

See: Glossary - Kinetic Energy

What is potential energy?

Potential energy is energy stored in a system due to position or configuration, capable of conversion to kinetic energy. Common types include gravitational potential energy (PE = mgh near Earth's surface, where h is height) and elastic potential energy (PE = ½kx² for springs, where k is spring constant and x is displacement). Potential energy is defined only for conservative forces where work done is path-independent. Changes in potential energy equal negative work done by the associated force. Understanding potential energy allows you to analyze situations using energy conservation instead of tracking forces throughout motion.

Example: A 10 kg object raised 5 meters gains 490 joules of gravitational potential energy (PE = mgh = 10 × 9.8 × 5 = 490 J), which converts to kinetic energy if dropped.

See: Glossary - Potential Energy

What is conservation of energy?

Conservation of Energy states that total energy in an isolated system remains constant, though it may transform between different forms. Energy cannot be created or destroyed—only converted from one form to another. For mechanical systems without friction, mechanical energy (kinetic plus potential) is conserved: E_initial = E_final, or KE_i + PE_i = KE_f + PE_f. When non-conservative forces like friction are present, mechanical energy decreases, converting to thermal energy, but total energy (including thermal) remains constant. Conservation of Energy is one of the most fundamental principles in physics, applicable from quantum mechanics to cosmology.

Example: A falling apple converts gravitational potential energy into kinetic energy, with total mechanical energy constant (ignoring air resistance). At any height h with velocity v: mgh + ½mv² = constant.

See: Glossary - Conservation of Energy

What is momentum?

Momentum is the product of an object's mass and velocity (p = mv), a vector quantity representing quantity of motion. Momentum has magnitude and direction, measured in kg·m/s. Objects with large mass or high velocity have large momentum and are hard to stop. Momentum is conserved in isolated systems—total momentum before interaction equals total momentum after (Conservation of Momentum). This makes momentum especially useful for analyzing collisions and explosions. Momentum connects to Newton's Second Law: net force equals rate of momentum change (F = dp/dt).

Example: A 1000 kg car traveling at 20 m/s has 20,000 kg·m/s of momentum in the direction of motion. Stopping it requires impulse equal to this momentum change.

See: Glossary - Linear Momentum and Chapter 7 - Momentum

What is conservation of momentum?

Conservation of Momentum states that total momentum in an isolated system remains constant when no external forces act. For a system of objects: p_total,initial = p_total,final, or m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f. This principle applies to collisions (objects interacting) and explosions (objects separating). Conservation of Momentum is especially powerful because it doesn't require knowing details of interaction forces—you only need initial and final states. The principle holds even when kinetic energy isn't conserved (inelastic collisions). Conservation of Momentum, along with Conservation of Energy, are the two most fundamental conservation laws in physics.

Example: In a collision between two billiard balls, total momentum before impact equals total momentum after impact, even though individual ball momenta change.

See: Glossary - Conservation of Momentum

What is friction?

Friction is a contact force that opposes relative motion or attempted motion between surfaces. It arises from microscopic interactions between surface irregularities. There are two types: static friction prevents surfaces at rest from sliding (up to maximum value f_s,max = μ_s N), while kinetic friction opposes surfaces already sliding (f_k = μ_k N). Here μ is coefficient of friction and N is normal force. Friction is parallel to surfaces and opposes motion direction. While friction causes energy loss in many systems, it's also essential—without friction, you couldn't walk, cars couldn't turn, and nails couldn't hold boards together.

Example: Friction between brake pads and rotors converts a car's kinetic energy into thermal energy, causing it to slow down and stop.

See: Glossary - Friction and Chapter 5 - Friction

What is projectile motion?

Projectile motion is two-dimensional motion of objects launched into air, combining constant horizontal velocity with constant vertical acceleration due to gravity. Horizontal and vertical motions are independent: horizontally, velocity is constant (no acceleration); vertically, acceleration is -g = -9.8 m/s² downward. The trajectory is parabolic. To analyze projectile motion: resolve initial velocity into horizontal (v_x = v₀ cos θ) and vertical (v_y = v₀ sin θ) components, apply kinematic equations independently to each direction, and combine results. Projectile motion applies to thrown balls, kicked soccer balls, fired bullets (ignoring air resistance), and many real-world situations.

Example: A basketball's arc from shooter to hoop follows projectile motion—constant horizontal velocity combined with downward gravitational acceleration creates the parabolic path.

See: Glossary - Projectile Motion and Chapter 3 - Projectile Motion

What are waves?

Waves are disturbances that propagate through space and time, transferring energy without transferring matter. Mechanical waves require a medium (water waves, sound waves, waves on strings); electromagnetic waves don't (light, radio waves). Waves can be transverse (particle displacement perpendicular to wave direction, like light) or longitudinal (particle displacement parallel to wave direction, like sound). Key wave properties include wavelength (distance between corresponding points), frequency (oscillations per second), amplitude (maximum displacement), and wave speed (v = fλ). Waves exhibit phenomena like interference, diffraction, and reflection. Understanding waves is essential for optics, sound, and quantum mechanics.

Example: Ocean waves are mechanical waves requiring water as medium; they cannot travel through empty space. Particles bob up and down as wave passes, but don't travel forward with the wave.

See: Chapter 10 - Waves and Glossary - Mechanical Waves

What is interference?

Interference is the combination of two or more waves occupying the same space simultaneously, following the superposition principle (net displacement equals sum of individual displacements). Constructive interference occurs when crests align with crests and troughs with troughs, producing increased amplitude. Destructive interference occurs when crests align with troughs, producing reduced or zero amplitude. Interference creates characteristic patterns (like alternating bright and dark bands in light) that prove wave nature. Interference is used in technologies like noise-canceling headphones and interferometers. Understanding interference is crucial for wave analysis and applications.

Example: Two speakers playing the same frequency create louder sound at positions where waves arrive in phase (constructive interference) and quieter sound where waves arrive out of phase (destructive interference).

See: Glossary - Wave Interference

Technical Detail Questions

What are SI units and why are they important?

SI (International System of Units) provides standardized base units for physical quantities, ensuring scientists worldwide can communicate precisely. The seven SI base units are: meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity). All other units are derived from these base units. Using SI units prevents conversion errors, facilitates international collaboration, ensures measurement consistency, and simplifies calculations (metric system uses powers of 10). While some countries use other systems (like US customary), SI is the global scientific standard.

Example: Speed is measured in m/s (derived from base units meter and second), force in newtons (N = kg·m/s²), and energy in joules (J = kg·m²/s²).

See: Glossary - SI Units and Chapter 1 - SI Units

What are significant figures and why do they matter?

Significant figures are the number of digits in a measurement that carry meaningful information about precision. They communicate measurement uncertainty: more significant figures indicate higher precision. Rules: non-zero digits are always significant; zeros between non-zero digits are significant; leading zeros are not significant; trailing zeros after decimal are significant. In calculations: multiplication/division result has as many sig figs as the least precise input; addition/subtraction result rounds to the least precise decimal place. Using significant figures correctly prevents false precision—reporting more digits than your measurement justifies misleads readers about accuracy.

Example: Measuring 15.20 cm (four significant figures) indicates greater precision than 15 cm (two significant figures). The first measurement is certain to ±0.01 cm, the second only to ±1 cm.

See: Glossary - Significant Figures

What is dimensional analysis?

Dimensional analysis is a mathematical technique using unit relationships to check equation validity and convert between measurement systems. Every physical quantity has dimensions (combinations of length L, mass M, time T, etc.). Equations must be dimensionally consistent—both sides must have same dimensions. To convert units: multiply by conversion factors (ratios equal to 1) that cancel unwanted units and introduce desired units. Dimensional analysis catches errors in equations (wrong dimensions indicate mistakes), validates derived formulas, and performs conversions systematically. It's an essential problem-solving tool throughout physics.

Example: Converting 60 mph to m/s: 60 miles/hr × (1609 m/mile) × (1 hr/3600 s) = 26.8 m/s. Units cancel algebraically, leaving correct result.

See: Glossary - Dimensional Analysis

What is the difference between precision and accuracy?

Accuracy measures how close measurements are to the true value—high accuracy means small systematic error. Precision measures how close repeated measurements are to each other—high precision means small random error. Measurements can be: (1) accurate and precise (clustered near true value), (2) precise but not accurate (clustered away from true value—systematic error), (3) accurate but not precise (scattered around true value), or (4) neither accurate nor precise. Ideal measurements are both accurate and precise. Understanding this distinction is crucial for error analysis and experimental design.

Example: A miscalibrated scale giving readings clustered around 105 g for a 100 g mass is precise (repeatable) but not accurate (wrong by 5 g systematically).

See: Glossary - Precision vs Accuracy

How do I add vectors?

Vectors add using two equivalent methods: (1) Graphical (head-to-tail): place second vector's tail at first vector's head, draw resultant from first tail to second head; (2) Component: resolve each vector into x and y components, add corresponding components separately (R_x = A_x + B_x, R_y = A_y + B_y), then find resultant magnitude (R = √(R_x² + R_y²)) and direction (θ = tan⁻¹(R_y/R_x)). Component method is more accurate and extends easily to three dimensions. Vector addition is commutative (order doesn't matter) but not performed like scalar addition—direction matters.

Example: Walking 3 m east (A = 3î) then 4 m north (B = 4ĵ) results in resultant displacement R = 5 m at 53° north of east (using Pythagorean theorem: R = √(3² + 4²) = 5).

See: Glossary - Vector Addition

What are vector components?

Vector components are projections of a vector along perpendicular coordinate axes (typically x and y). For vector A at angle θ from horizontal: horizontal component A_x = A cos θ, vertical component A_y = A sin θ. Components are scalars (have + or - signs indicating direction). Any vector can be uniquely decomposed into components; conversely, components uniquely determine a vector. Component notation makes vector calculations algebraic instead of geometric. Understanding components is essential for solving projectile motion, force analysis, and any two-dimensional problem.

Example: A 100 N force at 30° above horizontal has horizontal component 100 cos(30°) = 86.6 N and vertical component 100 sin(30°) = 50 N.

See: Glossary - Vector Components

What is free fall?

Free fall is motion under the sole influence of gravity, with acceleration equal to g = 9.8 m/s² downward regardless of mass. In free fall, all objects accelerate identically—a hammer and feather fall at the same rate in vacuum (Galileo's insight, famously demonstrated on the Moon). Free fall includes: objects dropped from rest, objects thrown upward (on the way up, at peak, and on way down), and objects thrown at angles (vertical component only). Air resistance complicates real-world free fall, but is negligible for dense, compact objects at low speeds. Free fall introduces constant acceleration, basis for kinematic equations.

Example: A dropped hammer and feather fall at the same rate in vacuum, both accelerating at 9.8 m/s² downward, demonstrating that gravitational acceleration is mass-independent.

See: Glossary - Free Fall

What are kinematic equations?

Kinematic equations are a set of four equations relating displacement (Δx), initial velocity (v₀), final velocity (v), acceleration (a), and time (t) for constant acceleration motion:

1. v = v₀ + at
2. Δx = v₀t + ½at²
3. v² = v₀² + 2aΔx
4. Δx = ½(v₀ + v)t

Each equation involves four of the five variables. Choose the equation with your three knowns and one unknown. These equations apply only when acceleration is constant. They're fundamental for solving kinematics problems—one-dimensional motion, free fall, and one direction at a time in projectile motion.

Example: Using v² = v₀² + 2aΔx, an object starting at rest (v₀ = 0) and accelerating at 2 m/s² travels 50 meters to reach v = √(2 × 2 × 50) = 14.1 m/s.

See: Glossary - Kinematic Equations

What is centripetal force?

Centripetal force is the net force directed toward the center of circular motion that causes an object to follow a curved path rather than traveling straight (F_c = mv²/r, where v is speed and r is radius). Centripetal means "center-seeking." It's not a new type of force—it's the net force from actual forces (tension, gravity, friction, normal force) that happens to point toward the center. Common mistake: there's no "centrifugal force" pushing outward in an inertial reference frame—that's just inertia (objects want to go straight per Newton's First Law). Understanding centripetal force is essential for analyzing circular motion.

Example: Earth's gravity provides the centripetal force keeping the Moon in its nearly circular orbit, constantly pulling Moon toward Earth and curving its path.

See: Glossary - Centripetal Force

What is torque?

Torque is the rotational effect of a force, equal to the product of force and perpendicular distance from rotation axis (τ = r⊥ F, or τ = rF sin θ where θ is angle between r and F). Torque measures the force's effectiveness at causing rotation, measured in N·m. Larger forces, longer lever arms, or more perpendicular application produce more torque. Torque is the rotational analog of force: just as force causes linear acceleration (F = ma), torque causes angular acceleration (τ = Iα). Understanding torque is essential for analyzing rotating systems like wheels, gears, seesaws, and wrenches.

Example: Applying 100 N at the end of a 0.3 m wrench produces 30 N·m of torque (τ = 0.3 × 100 = 30) to tighten a bolt. Pushing twice as far from the bolt would double the torque.

See: Glossary - Torque

What is angular velocity?

Angular velocity is the rate of change of angular displacement with respect to time, measured in radians per second (rad/s). It indicates how fast something rotates. For an object rotating with angular velocity ω: every point at radius r from axis has tangential velocity v = rω. Angular velocity is the rotational analog of linear velocity. Positive ω indicates counterclockwise rotation (by convention); negative indicates clockwise. All points on a rigid rotating object share the same angular velocity but different tangential velocities (points farther from axis move faster). Angular velocity is fundamental for rotational kinematics.

Example: A Ferris wheel rotating at ω = 0.1 rad/s completes one full revolution (2π radians) every 2π/0.1 = 62.8 seconds. A person 10 m from center has tangential velocity 1 m/s.

See: Glossary - Angular Velocity

What is simple harmonic motion?

Simple harmonic motion (SHM) is periodic motion where restoring force is proportional to displacement from equilibrium (F = -kx), producing sinusoidal position-time behavior. Key characteristics: motion repeats with period T, position varies as x = A cos(ωt + φ) where A is amplitude, ω is angular frequency, and φ is phase constant. Velocity and acceleration are also sinusoidal, with velocity maximum at equilibrium (x = 0) and acceleration maximum at extremes (x = ±A). SHM appears in mass-spring systems, pendulums (small angles), vibrating molecules, and many other systems. It's the simplest oscillatory motion and a foundation for understanding more complex vibrations.

Example: A mass on a spring oscillates with SHM, with position x = A cos(ωt) where ω = √(k/m). The motion is perfectly sinusoidal with period T = 2π/ω.

See: Glossary - Simple Harmonic Motion

What is resonance?

Resonance is the dramatic amplitude increase when driving frequency matches a system's natural frequency. Every oscillating system has natural frequencies at which it "wants" to vibrate. When driven at a natural frequency, even small periodic forces build up large amplitudes because energy adds constructively each cycle. Resonance occurs in mechanical systems (swings, bridges, buildings), acoustic systems (musical instruments, organ pipes), and electromagnetic systems (radio tuning). Resonance can be beneficial (amplifying desired signals) or destructive (causing structural failure). Understanding resonance is crucial for engineering and acoustics.

Example: Pushing a swing at its natural frequency causes amplitude to build dramatically with each push, demonstrating resonance. Pushing at other frequencies is much less effective.

See: Glossary - Resonance

What is the Doppler effect?

The Doppler effect is the change in observed frequency of a wave due to relative motion between source and observer. When source and observer move closer: observed frequency increases (higher pitch for sound, blue-shift for light). When they move apart: observed frequency decreases (lower pitch, red-shift). The effect occurs for all waves but is most familiar with sound. For source moving at speed v_s toward stationary observer: f_observed = f_source × c/(c - v_s), where c is wave speed. Doppler effect applications include police radar, astronomy (measuring star velocities), and medical ultrasound.

Example: An ambulance siren sounds higher pitched as it approaches you (frequency increases) and lower pitched as it moves away (frequency decreases), even though the siren emits constant frequency.

See: Glossary - Doppler Effect

What is refraction?

Refraction is the bending of waves when entering a medium with different wave speed, due to wavelength change while frequency remains constant. Light slows when entering denser media (like glass or water), causing it to bend toward the normal (perpendicular to surface). Snell's Law quantifies refraction: n₁ sin θ₁ = n₂ sin θ₂, where n is index of refraction (ratio of light speed in vacuum to speed in medium) and θ is angle from normal. Refraction explains why objects underwater appear at different positions, how lenses work, and why prisms separate white light into colors (dispersion). Understanding refraction is essential for optics.

Example: A straw in water appears bent at the surface due to light refraction between air and water. Light changes direction at the interface because it travels at different speeds in the two media.

See: Glossary - Refraction and Chapter 11 - Refraction

What is the difference between real and virtual images?

Real images form where light rays actually converge—they can be projected onto screens and captured by cameras. Concave mirrors and convex lenses can form real images when object is beyond focal point. Real images are inverted (upside down). Virtual images form where light rays appear to diverge from—they cannot be projected onto screens but can be seen by looking into the optical device. Plane mirrors, convex mirrors, and concave lenses always form virtual images. Convex lenses form virtual images when object is inside focal point. Virtual images are upright. Understanding this distinction is crucial for ray tracing and image formation analysis.

Example: A movie projector creates real images on the screen as light rays from film converge through the lens. Your bathroom mirror reflection is a virtual image appearing behind the mirror where light rays don't actually converge.

See: Glossary - Real Images and Glossary - Virtual Images

What is electric charge?

Electric charge is a fundamental property of matter that causes electromagnetic interactions, existing in positive and negative forms. Electrons carry negative charge (-1.6 × 10⁻¹⁹ coulombs); protons carry equal positive charge. Like charges repel; opposite charges attract. Charge is quantized (comes in discrete packets, multiples of fundamental charge e) and conserved (total charge in isolated system never changes—charge transfers between objects but isn't created or destroyed). Charging methods include friction (rubbing), contact (touching), and induction (no contact). Understanding charge is foundational for electricity and magnetism.

Example: Rubbing a balloon on hair transfers electrons to balloon, leaving hair positively charged and balloon negatively charged. They attract due to opposite charges.

See: Glossary - Electric Charge and Chapter 12 - Electric Charge

What is an electric field?

An electric field is a region around charged objects where electric forces act on other charges, represented by force per unit charge (E = F/q). Electric field is a vector pointing in the direction positive test charge would be pushed. Field lines visualize electric fields: they emerge from positive charges, terminate on negative charges, and never cross. Line density indicates field strength. Electric field allows us to think about charges creating fields that then exert forces on other charges, separating the "source" from the "test" charge. Understanding electric fields is essential for analyzing electrostatic situations.

Example: The electric field around a positive point charge points radially outward and weakens with distance according to E = kq/r². A positive test charge placed in this field experiences outward force.

See: Glossary - Electric Field

Common Challenge Questions

Why do I need to learn physics formulas instead of just looking them up?

While you can look up formulas, understanding them deeply allows you to: (1) recognize when and how to apply them, (2) identify which of multiple formulas applies to a situation, (3) manipulate equations to solve for different variables, (4) catch errors if you write formulas incorrectly, (5) understand physical relationships they represent, and (6) derive variations for novel situations. Memorization without understanding is useless—you'll misapply formulas. Deep understanding comes from working many problems, seeing connections between concepts, and recognizing patterns. The goal isn't mindless recall but internalized physical intuition that lets formulas become tools for thinking, not just calculations to perform.

How do I know which kinematic equation to use?

Choose the kinematic equation that contains your three known variables and your one unknown. Strategy: (1) list what you know (Δx, v₀, v, a, t), (2) identify what you're solving for, (3) select the equation containing your three knowns and one unknown. The four equations are: v = v₀ + at (no Δx), Δx = v₀t + ½at² (no v), v² = v₀² + 2aΔx (no t), Δx = ½(v₀ + v)t (no a). Sometimes you'll solve one equation first to find an intermediate variable, then use a second equation for the final answer. This systematic approach works reliably—don't guess randomly or try to memorize specific scenarios.

Why is the normal force not always equal to weight?

Normal force is the perpendicular contact force a surface exerts on an object, preventing objects from passing through each other. While N = mg for objects resting on horizontal surfaces, normal force adjusts to satisfy Newton's Second Law based on all forces and motion. Examples where N ≠ mg: (1) on inclined planes, N = mg cos θ where θ is angle, (2) in elevators accelerating upward, N > mg (feel heavier), (3) in elevators accelerating downward, N < mg (feel lighter), (4) at the top of vertical circles, N + mg provides centripetal force. The key insight: normal force is whatever value needed (along with other forces) to produce the actual acceleration. Don't assume N = mg—analyze forces carefully.

How do I draw a free-body diagram?

A free-body diagram (FBD) shows all forces acting on ONE object, representing forces as arrows with lengths proportional to magnitudes. Steps: (1) Isolate the object—draw a dot or simple shape representing it, (2) Identify all forces acting ON the object (not BY the object), (3) Draw force vectors as arrows originating from the object, pointing in force directions, (4) Label each force (F_gravity, F_normal, F_tension, F_friction, etc.), (5) Choose coordinate system (usually x horizontal, y vertical or along/perpendicular to surfaces). Don't include motion or equal-opposite pairs (those act on different objects). FBDs are essential for applying Newton's Laws—they help you visualize forces and set up equations correctly.

Why does an object at terminal velocity have zero acceleration but constant velocity?

Terminal velocity occurs when drag force (air resistance) increases with speed until it equals weight, making net force zero. By Newton's Second Law (F_net = ma), zero net force means zero acceleration. Zero acceleration means velocity isn't changing—it's constant. The object continues falling at constant velocity because balanced forces produce no acceleration, while the constant velocity is maintained by inertia (Newton's First Law). This illustrates the distinction between velocity and acceleration: velocity tells current motion; acceleration tells if motion is changing. Terminal velocity demonstrates dynamic equilibrium—moving at constant velocity with balanced forces.

How can kinetic energy be lost in inelastic collisions if energy is conserved?

Energy is always conserved—it never disappears. In inelastic collisions, kinetic energy isn't lost; it transforms into other forms (primarily thermal energy and sound, possibly deformation energy). The objects heat up slightly due to friction during collision, acoustic waves carry energy away, and permanent deformations store energy in changed molecular configurations. "Kinetic energy isn't conserved" means mechanical kinetic energy specifically decreases, but total energy (kinetic + thermal + sound + deformation) remains constant. In perfectly inelastic collisions (objects stick), maximum kinetic energy converts to other forms. This distinction is crucial: momentum is always conserved (isolated system); kinetic energy is conserved only in elastic collisions; total energy is always conserved.

Why do I need to resolve forces into components?

Component resolution (breaking forces into perpendicular x and y parts) transforms two-dimensional vector problems into two independent one-dimensional scalar problems, which are much easier to solve. It allows you to apply Newton's Second Law separately in perpendicular directions: ΣF_x = ma_x and ΣF_y = ma_y. This works because perpendicular components don't affect each other—horizontal forces don't cause vertical acceleration and vice versa. Component resolution is essential for inclined planes (resolve weight into parallel and perpendicular components), projectile motion (horizontal and vertical are independent), and any situation with forces at angles. Master this technique—it's fundamental to physics problem-solving.

How do I analyze circular motion problems?

For uniform circular motion (constant speed around circle): (1) recognize centripetal acceleration points toward center with magnitude a_c = v²/r, (2) identify all actual forces acting on object (tension, gravity, normal, friction), (3) resolve forces into radial (toward center) and tangential (perpendicular to radius) components, (4) apply Newton's Second Law in radial direction: ΣF_radial = ma_c = mv²/r, (5) solve for unknown (often speed or tension). Don't include "centrifugal force" pointing outward—that's not a real force in inertial frames. For non-uniform circular motion (changing speed), also analyze tangential direction where tangential forces cause changes in speed. Circular motion problems become straightforward with systematic component analysis.

Why does a pendulum's period not depend on mass?

For a simple pendulum (point mass on massless string), period T = 2π√(L/g) depends only on length L and gravitational acceleration g, not mass m. This occurs because both restoring force and inertia are proportional to mass—they cancel in the equations. Heavier masses experience stronger restoring forces (F = -mg sin θ ≈ -mgθ for small angles) but also have more inertia resisting acceleration. The ratio F/m = gθ is mass-independent. Consequence: all simple pendulums of the same length at the same location have identical periods. This beautiful result, discovered by Galileo, demonstrates how mass affects force and inertia proportionally. Note: this applies to simple pendulums; physical pendulums (extended objects) have different analysis.

How do standing waves form?

Standing waves form through interference of waves traveling in opposite directions with the same frequency, typically from a wave and its reflection. At certain frequencies (resonant frequencies), the forward and reflected waves interfere constructively and destructively at fixed locations, creating a stationary pattern with nodes (zero amplitude points) and antinodes (maximum amplitude points). Standing waves on strings: L = nλ/2 where n = 1, 2, 3... gives resonant wavelengths. Standing waves are crucial for musical instruments: guitar strings, organ pipes, drums all vibrate at characteristic frequencies determined by their dimensions. Understanding standing waves requires grasping superposition and boundary conditions.

Example: A guitar string vibrates in standing wave patterns with nodes at both fixed ends and antinodes where amplitude is maximum. The fundamental (n=1) has one antinode; higher harmonics have more.

See: Glossary - Standing Waves

When should I use energy methods versus force methods?

Use energy methods (Conservation of Energy, Work-Energy Theorem) when: (1) you need initial and final states without detailed path information, (2) forces vary with position (like springs), (3) motion involves transformations between kinetic and potential energy, (4) you want simpler calculations avoiding acceleration and time. Use force methods (Newton's Second Law) when: (1) you need acceleration, forces, or time information, (2) motion involves constant forces, (3) you're analyzing equilibrium (zero acceleration), (4) energy is dissipated by friction (though work by friction can be handled in energy approach). Often, problems can be solved either way—choose the method that leads to fewer steps. Many complex problems combine both approaches strategically.

Best Practice Questions

What problem-solving strategy should I use for physics problems?

Follow this systematic approach: (1) Read carefully, visualizing the situation; (2) Sketch a diagram showing the setup, coordinate system, and known values; (3) List knowns and unknowns explicitly; (4) Plan which principles/equations apply (kinematics, Newton's Laws, energy, momentum); (5) Solve algebraically first (don't plug numbers yet), manipulating equations to isolate the unknown; (6) Calculate using known values with units; (7) Check whether the answer makes physical sense (right order of magnitude, correct units, physically reasonable). This structured approach prevents careless errors, helps you learn problem patterns, and makes complex problems manageable. Don't skip to calculations—the thinking steps are most important.

How should I approach laboratory work?

Effective laboratory work involves: (1) Prepare by reading lab instructions beforehand, understanding objectives and procedures; (2) Hypothesize predicting results before observing; (3) Observe carefully during experiments, taking detailed notes; (4) Measure systematically with appropriate precision, recording uncertainties; (5) Analyze data promptly while fresh in memory, creating graphs and calculating results; (6) Compare experimental results with theoretical predictions, explaining discrepancies; (7) Reflect on what worked, what didn't, and what you learned. Keep detailed lab notebooks with dates, conditions, raw data, calculations, and observations. Lab work teaches scientific method, data analysis, and how physics concepts apply practically—approach it as seriously as theoretical study.

How can I improve my conceptual understanding?

Deepen understanding through multiple approaches: (1) Explain concepts aloud or in writing to others—teaching reveals gaps in understanding; (2) Visualize using diagrams, graphs, and MicroSims—physical intuition complements mathematical rigor; (3) Connect new concepts to previous learning and everyday experiences; (4) Question assumptions and explore edge cases (what happens if...?); (5) Work many problems of varying difficulty; (6) Study worked examples actively, covering the solution and trying yourself; (7) Use the learning graph to see how concepts relate. Conceptual understanding goes beyond formula manipulation—it means you can explain why methods work, predict outcomes, and apply knowledge flexibly to novel situations.

When should I use the learning graph?

Use the learning graph: (1) Before studying a new chapter to identify prerequisites you should review; (2) When stuck on a concept to trace back to foundational ideas you might be missing; (3) For review to see connections between concepts and study systematically; (4) When planning study sessions to tackle concepts in logical order; (5) For overview to understand course structure and where topics fit. The learning graph shows concept dependencies—arrows point from prerequisites to dependent concepts. If struggling with a concept, check what it depends on and ensure you've mastered those first. The interactive viewer lets you search, filter by category, and explore paths through the material.

See: Interactive Learning Graph Viewer

How do I effectively use MicroSims?

Maximize MicroSim learning value by: (1) Predict before manipulating—what do you expect to happen?; (2) Observe carefully when changing variables, noting patterns and relationships; (3) Test systematically varying one parameter at a time to isolate effects; (4) Quantify relationships when possible (doubling X doubles Y, etc.); (5) Connect simulations to theoretical equations—see how formulas manifest visually; (6) Apply to real-world scenarios mentally (how does this explain...?). Don't just play randomly—approach MicroSims as virtual labs with learning objectives. They're most effective when integrated with reading and problem-solving, not used in isolation. Come back to MicroSims after studying theory to reinforce understanding.

How should I prepare for assessments?

Effective preparation strategies: (1) Start early, reviewing regularly rather than cramming—distributed practice enhances retention; (2) Use active recall, testing yourself instead of passively rereading; (3) Practice problems extensively—physics competence requires doing, not just understanding; (4) Study conceptually, understanding why methods work rather than memorizing procedures; (5) Identify weak areas through practice tests and targeted review; (6) Create summary sheets with key equations, concepts, and problem-solving strategies; (7) Study with peers, explaining concepts to each other and comparing problem approaches. On assessments, read questions carefully, draw diagrams, show work clearly, check units and reasonableness. Remember assessments span all Bloom's levels—prepare for application, analysis, and evaluation questions, not just recall.

How do I build physical intuition?

Physical intuition—gut feeling for how systems behave—develops through: (1) Experience observing and interacting with physical systems in labs and daily life; (2) Visualization mentally simulating scenarios before calculating; (3) Estimation making quick order-of-magnitude predictions to catch calculation errors; (4) Pattern recognition seeing similarities across different problems; (5) Limiting cases checking what happens at extremes (very large, very small, zero); (6) Analogies connecting abstract concepts to familiar experiences. Strong intuition lets you catch errors, make reasonable approximations, and approach novel problems confidently. It complements mathematical rigor—trust your intuition to guide problem-solving, then verify with calculations. Intuition grows with practice and reflection.

What's the best way to organize my physics notes?

Effective note organization: (1) Date entries and include chapter/topic references for easy location; (2) Separate class notes, reading notes, problem solutions, and lab reports; (3) Use consistent formatting with headings, subheadings, and visual hierarchy; (4) Include diagrams, graphs, and examples—not just text and equations; (5) Highlight key equations, definitions, and problem-solving strategies; (6) Cross-reference related concepts and where they connect; (7) Leave white space for additions and corrections; (8) Review and annotate notes regularly, adding insights from problem-solving. Consider digital notes for searchability or paper notes for better retention—choose what works for you. Good notes become invaluable study resources for exams and reference material for future courses.

How can I check if my answer is reasonable?

Always perform reasonableness checks: (1) Units: Do units work out correctly? (2) Sign: Is direction (positive/negative) sensible? (3) Magnitude: Is the order of magnitude reasonable? (Compare to familiar values: human speeds ~1-10 m/s, car speeds ~10-30 m/s, g ≈ 10 m/s²); (4) Limiting cases: What happens at extremes? (If v → 0, does kinetic energy → 0?); (5) Symmetry: Do symmetric situations give symmetric results?; (6) Comparison: Does this match similar problems you've solved? Catching errors through reasonableness checks is a crucial skill—computers calculate perfectly but can't detect if you used the wrong equation or set up the problem incorrectly. Develop this habit early.

Advanced Topic Questions

How does conservation of energy apply when friction is present?

When friction acts, mechanical energy (kinetic + potential) isn't conserved—it decreases, converting to thermal energy. Total energy (mechanical + thermal) remains conserved. To analyze: (1) Calculate work done by friction: W_friction = -f_k × d (negative because it opposes motion); (2) Apply modified energy conservation: KE_i + PE_i + W_friction = KE_f + PE_f, where W_friction is negative; (3) Recognize that |W_friction| equals thermal energy generated. Alternatively, track total energy: E_mechanical,initial = E_mechanical,final + E_thermal. Friction problems often involve finding stopping distances, final speeds after energy loss, or heat generated. The key insight: energy never disappears—it transforms into forms (thermal, sound) not always tracked explicitly as mechanical energy.

How do I analyze multi-object systems using conservation principles?

For systems of multiple interacting objects: (1) Define the system boundary including all relevant objects; (2) Identify whether external forces act on the system (if none, momentum is conserved); (3) Identify whether non-conservative forces act (if none, mechanical energy is conserved); (4) Write conservation equations for the entire system, not individual objects; (5) Solve system of equations for unknowns. Example: in collisions, momentum is always conserved if no external forces; energy is conserved only if elastic. For connected objects (Atwood machines, pulleys), use constraints (like rope length constancy) to relate motion. System analysis is powerful because it avoids tracking internal forces—they cancel in pairs per Newton's Third Law.

How do rotational and translational motion relate in rolling?

Rolling without slipping is combined rotational and translational motion satisfying the constraint v_cm = rω, where v_cm is center of mass velocity, r is radius, and ω is angular velocity. This constraint means the contact point has zero instantaneous velocity (it's momentarily at rest relative to ground). Rolling objects have both translational kinetic energy (½mv_cm²) and rotational kinetic energy (½Iω²), so total KE = ½mv_cm² + ½Iω². When analyzing rolling down inclines, use energy conservation including both forms of kinetic energy. The rolling constraint couples translational and rotational motion—they're not independent. Objects with different mass distributions (different I) roll at different rates even with same mass and radius.

What causes tides and how do they relate to physics concepts?

Tides arise from differential gravitational forces: the Moon's gravity is slightly stronger on Earth's near side (pulling water toward Moon) and slightly weaker on far side (Earth center pulled more than far-side water, effectively stretching). This creates two tidal bulges—one toward Moon, one away. Earth rotates under these bulges, producing two high tides and two low tides daily. Tidal forces also act on Earth itself (earth tides) and cause tidal locking (Moon always shows same face to Earth). Tides demonstrate: (1) gravitational force decreases with distance (inverse square law), (2) reference frame effects (far-side bulge seems counterintuitive), (3) system energy dissipation (tides gradually slow Earth's rotation and increase Moon's orbital distance). Solar tides also exist; spring tides occur when Sun and Moon align.

How do waves transfer energy without transferring matter?

Waves propagate by passing energy from particle to particle through a medium (or through electromagnetic fields for EM waves). Each particle oscillates about an equilibrium position, executing simple harmonic motion, then transfers energy to neighbors. The particle itself doesn't travel with the wave—it just moves back and forth. Energy flows continuously through space while matter oscillates locally. Example: water waves appear to move water forward, but floating objects show water actually moves in circles, returning to nearly original positions. Wave speed depends on medium properties (tension, density, elasticity) that determine how quickly energy transfers between particles. Understanding this distinction is crucial: wave phenomena involve energy transport, not mass transport.

What are the limits of classical physics?

Classical physics (Newton's Laws, Maxwell's Equations) works excellently for everyday objects moving at ordinary speeds. It fails at extremes: (1) Very fast (approaching light speed): Relativistic effects become important—time dilates, lengths contract, mass increases, nothing travels faster than c. Classical mechanics is replaced by special relativity; (2) Very small (atomic scale): Quantum effects dominate—particles behave like waves, energy is quantized, uncertainty principle applies. Classical mechanics is replaced by quantum mechanics; (3) Very massive (black holes, cosmology): Spacetime curvature matters. Classical gravity is replaced by general relativity. For everyday human-scale phenomena (speeds << c, sizes >> atoms), classical physics is accurate and simpler than relativistic or quantum treatments. Know when approximations apply and when they break down.

How do conservative and non-conservative forces differ fundamentally?

Conservative forces (gravity, elastic, electric) have work path-independent—work depends only on initial and final positions, allowing potential energy definition. Moving in closed loop against conservative force returns to same energy state (zero net work). Mathematical property: conservative forces have zero curl (∇ × F = 0). Non-conservative forces (friction, air resistance, tension) have path-dependent work—work depends on specific path taken. Moving in closed loop against friction dissipates energy. You can't define potential energy for non-conservative forces because there's no unique value at each position. Physically: conservative forces store energy retrievably; non-conservative forces dissipate energy into thermal and other forms. This distinction determines when mechanical energy conservation applies.

How would I design an experiment to measure gravitational acceleration?

Several approaches demonstrate experimental design: Method 1 (Simple pendulum): Measure period T for various lengths L, plot T² vs. L. Slope equals 4π²/g, so g = 4π²/(slope). Method 2 (Free fall): Drop object from measured heights h, time fall with photogate. Use h = ½gt² to find g = 2h/t². Repeat for multiple heights, plot h vs. t², slope gives ½g. Method 3 (Inclined plane): Release cart on frictionless track at angle θ, measure acceleration a_measured. Since a = g sin θ, we get g = a/sin θ. Each method requires: controlling variables, minimizing uncertainties, collecting multiple trials, analyzing data graphically, calculating uncertainties in results. This demonstrates how physical principles enable measurement of fundamental constants.

High School Physics Course FAQ

This FAQ addresses common questions about the course structure, core physics concepts, technical details, learning challenges, best practices, and advanced topics. Questions are organized by category and aligned with Bloom's Taxonomy cognitive levels to support progressive learning.

Getting Started Questions

What is this physics course about?

This is a comprehensive year-long high school physics course that develops scientific literacy through hands-on learning and systematic progression from foundational knowledge to creative application. The course covers classical mechanics, waves, optics, and electricity, structured using the Revised Bloom's Taxonomy (2001) to build cognitive skills from recalling fundamental principles to designing original experiments. You'll explore 200+ physics concepts through 12 chapters, extensive laboratory work, and interactive MicroSims that keep you engaged with real-world applications.

See the Course Description for complete details.

Who is this course designed for?

This course is designed for high school students in grades 10-12 who have completed Algebra II and Geometry. It's ideal for students who want a hands-on, engaging approach to physics that goes beyond memorization, emphasizing creative problem-solving, laboratory investigations, and real-world applications. Whether you're preparing for AP Physics, planning an engineering pathway, or simply curious about how the universe works, this course provides the foundation you need.

See Course Description for prerequisites and learning outcomes.

What prerequisites do I need?

You need to have successfully completed Algebra II and Geometry. These mathematics courses provide the essential skills for working with equations, graphing, trigonometry, and geometric relationships that are fundamental to physics problem-solving. No prior physics knowledge is required—we start with foundational concepts and build systematically.

See Course Description for detailed prerequisite information.

How is this course structured?

The course is organized into 12 chapters that progress logically through physics topics: (1) Scientific Foundations, (2-3) Motion in One and Two Dimensions, (4-5) Forces and Newton's Laws, (6) Work and Energy, (7) Momentum, (8) Rotational Motion, (9) Oscillations, (10) Waves and Sound, (11) Light and Optics, and (12) Electric Charge and Fields. Each chapter builds on previous concepts using a learning graph that maps concept dependencies, ensuring you master prerequisites before advancing to more complex topics.

See Chapters for the complete chapter listing.

What makes this textbook "intelligent"?

This textbook is considered "intelligent" because it uses a learning graph—a directed graph showing concept dependencies—to personalize your learning path. The learning graph ensures you understand prerequisite concepts before advancing, provides multiple pathways through the material, and can adapt to your individual needs. Additionally, the textbook includes interactive MicroSims (educational simulations), embedded assessments, and AI-generated content designed specifically for your learning level.

See Learning Graph for visualization and details.

How long will this course take?

As a year-long high school course, you should expect to invest approximately 5-7 hours per week including class time, laboratory work, homework, and projects. The course is designed for a standard 36-week academic year with two semesters. Each chapter requires 2-4 weeks depending on complexity, with additional time for major projects like the Rube Goldberg machine (Semester 1) and Physics TED Talk (Semester 2).

See Course Description for assessment framework and time commitments.

What materials and equipment do I need?

Beyond this textbook, you'll need a scientific calculator, notebook for lab reports, and access to a computer for MicroSims and online resources. Laboratory equipment is provided by your school's physics lab. For some projects, you may need to gather common household materials (rubber bands, springs, balls, etc.). All MicroSims run in a web browser—no special software required.

What are MicroSims and how do I use them?

MicroSims are interactive educational simulations embedded throughout the textbook that let you explore physics concepts hands-on. Each MicroSim focuses on a specific concept (like projectile motion or wave interference) and allows you to adjust parameters, run experiments, and visualize results in real-time. They're designed to complement laboratory work and help you develop intuition about physical phenomena before solving mathematical problems.

See MicroSims Index for all available simulations.

How are grades determined in this course?

Assessment is distributed across Bloom's Taxonomy levels: Remembering (10%), Understanding (15%), Applying (30%), Analyzing (20%), Evaluating (15%), and Creating (10%). You'll be evaluated through weekly quizzes, problem sets, laboratory analysis reports, peer reviews, and two major capstone projects. The emphasis is on demonstrating higher-order thinking skills rather than pure memorization, with substantial weight given to problem-solving and creative application.

See Course Description for the complete grading breakdown.

Can I use this textbook for self-study?

Yes! This textbook is designed to support self-directed learning through clear explanations, worked examples, interactive MicroSims, and comprehensive glossary terms. The learning graph helps you identify which concepts to study in which order. However, you'll get the most value from hands-on laboratory experiences, so consider partnering with a local school, science center, or online physics community for lab opportunities and peer discussion.

What topics are NOT covered in this course?

This course focuses on classical physics and does not cover Quantum Mechanics, Atomic Physics, Nuclear Physics, Solid State Physics, Digital Electronics, or Circuit Analysis. These advanced topics are typically covered in college-level physics courses or specialized electives. The course provides a strong foundation that prepares you for these advanced studies.

See Course Description for the complete list.

How do I navigate the learning graph?

The learning graph is an interactive visualization showing all 200 concepts as nodes, with arrows indicating prerequisite relationships. Click on any concept to see its definition, prerequisites (concepts you should learn first), and dependents (concepts that build upon it). Use the search function to find specific concepts, or filter by taxonomy (Foundation, Kinematics, Dynamics, etc.) to explore related topics. The graph viewer includes zoom, pan, and clustering features for easy navigation.

See Learning Graph Viewer for interactive exploration.

Core Concepts

What is the scientific method?

The scientific method is a systematic approach to investigating phenomena through observation, hypothesis formation, experimentation, and analysis. It provides a structured way to ask questions and find reliable answers about the natural world. The process typically includes: observing a phenomenon, researching existing knowledge, formulating a testable hypothesis, designing and conducting experiments, analyzing data, drawing conclusions, communicating results, and refining based on feedback. The scientific method is iterative—we cycle through these steps multiple times to refine our understanding.

See Chapter 1: Scientific Method for detailed explanation and examples.

What are SI units and why do we use them?

SI (Système International) units are the standardized international system of measurement used by scientists worldwide. The system is based on seven fundamental base units (meter, kilogram, second, ampere, kelvin, mole, candela) from which all other units are derived. We use SI units to ensure clear communication across languages and cultures, maintain consistency in calculations, and enable accurate comparison of experimental results. In physics, we primarily work with meters (length), kilograms (mass), and seconds (time).

See Chapter 1: SI Units and Glossary: SI Units.

What is the difference between scalars and vectors?

Scalars are physical quantities that have only magnitude (size), while vectors have both magnitude and direction. Examples of scalars include temperature (20°C), mass (5 kg), time (10 seconds), and speed (30 m/s). Examples of vectors include displacement (50 m north), velocity (30 m/s eastward), force (100 N downward), and acceleration (9.8 m/s² toward Earth's center). Vectors require special mathematical operations (vector addition, components, dot and cross products) that account for their directional nature.

See Chapter 1: Scalars and Vectors and Glossary: Scalars and Vectors.

What is displacement and how is it different from distance?

Displacement is a vector quantity representing the straight-line distance and direction from a starting position to an ending position, while distance is a scalar quantity measuring the total length of the path traveled regardless of direction. For example, if you walk 3 blocks north then 4 blocks east, your distance traveled is 7 blocks, but your displacement is 5 blocks northeast (using the Pythagorean theorem). Displacement tells you where you ended up relative to where you started; distance tells you how far you walked.

See Chapter 2: Displacement and Glossary: Displacement vs Distance.

What is velocity and how does it differ from speed?

Velocity is a vector quantity describing the rate of change of position, including both speed (magnitude) and direction, while speed is a scalar quantity measuring only how fast an object moves regardless of direction. A car traveling 60 km/h northward has a velocity that fully specifies its motion, whereas speed only tells you it's moving at 60 km/h. Two cars can have the same speed but different velocities if they're traveling in different directions. Velocity can be negative (indicating direction opposite to the positive reference direction) while speed is always positive.

See Chapter 2: Velocity and Glossary: Velocity vs Speed.

What is acceleration?

Acceleration is the rate of change of velocity with respect to time, measured in meters per second squared (m/s²). It describes how quickly an object's velocity is changing, which includes changes in speed, direction, or both. When a car speeds up, slows down, or turns a corner, it's accelerating. Acceleration can be positive (increasing velocity), negative (decreasing velocity, sometimes called deceleration), or perpendicular to motion (changing direction as in circular motion). Constant acceleration, like gravity near Earth's surface (9.8 m/s²), means velocity changes by the same amount each second.

See Chapter 2: Acceleration and Glossary: Acceleration.

What are Newton's Three Laws of Motion?

Newton's Three Laws form the foundation of classical mechanics. First Law (Inertia): An object at rest stays at rest and an object in motion stays in motion with constant velocity unless acted upon by a net external force. Second Law: The net force on an object equals its mass times acceleration (F = ma), meaning heavier objects require more force to accelerate. Third Law: For every action force, there is an equal and opposite reaction force acting on a different object. These laws explain everything from why seatbelts protect you in crashes to how rockets propel through space.

See Chapter 4: Newton's Laws and Glossary: Newton's First Law, Second Law, Third Law.

What is force and how is it measured?

Force is a vector quantity representing a push or pull that can cause an object to accelerate, measured in newtons (N). One newton is the force required to accelerate a 1-kilogram object at 1 meter per second squared. Forces can be contact forces (friction, tension, normal force) that require objects to touch, or field forces (gravity, electric, magnetic) that act at a distance. The net force (vector sum of all forces) determines an object's acceleration according to Newton's Second Law. Forces are measured using devices like spring scales, force sensors, or calculated from mass and acceleration.

See Chapter 4: Force and Glossary: Force.

What is friction and why is it important?

Friction is a force that opposes the relative motion or attempted motion between surfaces in contact. It arises from microscopic irregularities where surfaces interact. There are two main types: static friction (prevents motion from starting) and kinetic friction (opposes motion once started). Friction is essential for everyday activities—walking, driving, and holding objects all depend on friction. Without friction, you couldn't walk forward (your feet would slip), cars couldn't accelerate or brake, and nothing would stay in place. However, friction also causes energy loss and wear in machines, requiring lubrication and maintenance.

See Chapter 5: Friction and Glossary: Friction, Static Friction, Kinetic Friction.

What is work in physics?

Work is the transfer of energy that occurs when a force acts on an object through a displacement in the direction of the force, measured in joules (J). Work equals force times displacement times the cosine of the angle between them: W = F·d·cos(θ). Only the component of force parallel to displacement does work. Lifting a 20-kg box 1.5 meters requires 294 joules of work against gravity. Importantly, if there's no displacement (pushing against a wall that doesn't move) or if force is perpendicular to motion (centripetal force in circular motion), zero work is done despite effort expended.

See Chapter 6: Work and Glossary: Work.

What is energy and what forms does it take?

Energy is the capacity to do work or cause change, measured in joules. Energy exists in many forms but broadly divides into kinetic energy (energy of motion) and potential energy (stored energy due to position or configuration). Kinetic energy equals ½mv², where m is mass and v is velocity. Potential energy includes gravitational potential energy (mgh, where h is height), elastic potential energy (stored in springs and stretched materials), and electric potential energy (stored in separated charges). The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another.

See Chapter 6: Energy and Glossary: Kinetic Energy, Potential Energy.

What is momentum?

Momentum is the product of an object's mass and velocity, representing its quantity of motion, measured in kg·m/s. A 2-kg ball moving at 5 m/s has momentum of 10 kg·m/s. Momentum is a vector quantity pointing in the direction of velocity. Heavy objects moving fast have large momentum and are difficult to stop. The Law of Conservation of Momentum states that in an isolated system (no external forces), total momentum remains constant. This explains why in collisions between billiard balls, the total momentum before impact equals the total momentum after.

See Chapter 7: Momentum and Glossary: Linear Momentum.

What are collisions and what types exist?

Collisions are interactions where two or more objects exert forces on each other for a short time. Elastic collisions conserve both momentum and kinetic energy—objects bounce apart with no energy loss (billiard balls approximate this). Inelastic collisions conserve momentum but not kinetic energy—some energy converts to heat, sound, or deformation (car crashes). Perfectly inelastic collisions occur when objects stick together after impact, losing maximum kinetic energy while still conserving momentum (railroad cars coupling). All collision types obey conservation of momentum, but only elastic collisions conserve kinetic energy.

See Chapter 7: Collisions and Glossary: Elastic Collisions, Inelastic Collisions.

What is torque?

Torque is the rotational analog of force, causing objects to rotate about an axis. It equals the product of force and the perpendicular distance from the rotation axis (lever arm): τ = F·r·sin(θ). Measured in newton-meters (N·m), torque depends on both force magnitude and where it's applied—using a longer wrench increases torque for the same force. Opening a door is easier when you push far from the hinges (large lever arm) than near the hinges (small lever arm). Torque causes angular acceleration just as force causes linear acceleration, following τ = Iα where I is rotational inertia.

See Chapter 8: Torque and Glossary: Torque.

What is simple harmonic motion?

Simple harmonic motion (SHM) is oscillatory motion where the restoring force is directly proportional to displacement from equilibrium, following Hooke's Law (F = -kx). A mass on a spring exhibits SHM—when displaced and released, it oscillates sinusoidally with constant period and frequency. The motion is "simple" because the acceleration is always proportional to displacement but opposite in direction. Pendulums (for small angles), vibrating guitar strings, and atoms in molecules all exhibit SHM. Key characteristics include amplitude (maximum displacement), period (time per cycle), frequency (cycles per time), and conservation of mechanical energy as the system oscillates between kinetic and potential energy.

See Chapter 9: Simple Harmonic Motion and Glossary: Simple Harmonic Motion.

What are waves and how do they travel?

Waves are disturbances that transfer energy through a medium (mechanical waves) or through space (electromagnetic waves) without transferring matter. Waves have characteristic properties: wavelength (distance between crests), frequency (cycles per second), amplitude (maximum displacement), and speed (wavelength times frequency). Transverse waves have oscillations perpendicular to wave direction (light, waves on strings), while longitudinal waves have oscillations parallel to wave direction (sound). Waves can interfere (combine), reflect (bounce), refract (bend), and diffract (spread) depending on the medium and obstacles encountered.

See Chapter 10: Waves and Glossary: Mechanical Waves, Wave Properties.

What is sound?

Sound is a longitudinal mechanical wave that propagates through a medium (air, water, solids) as compressions and rarefactions. When you speak, your vocal cords vibrate, creating pressure variations that travel through air at approximately 343 m/s at room temperature. Sound cannot travel through vacuum because it requires a medium for propagation. We perceive frequency as pitch (high frequency = high pitch) and amplitude as loudness. Sound exhibits all wave behaviors: reflection (echoes), refraction (bending), diffraction (spreading around obstacles), and interference (beats when two frequencies are close).

See Chapter 10: Sound and Glossary: Sound Waves.

What is light and how does it behave?

Light is electromagnetic radiation in the visible portion of the spectrum (approximately 400-700 nm wavelength) that can be detected by the human eye. Light exhibits wave-particle duality—behaving as both a wave (showing interference and diffraction) and as particles called photons. Light travels at approximately 3.0 × 10⁸ m/s in vacuum, the fastest speed possible in the universe. Light behaves as a transverse wave with oscillating electric and magnetic fields perpendicular to its direction of travel. It undergoes reflection (mirrors), refraction (lenses), dispersion (prisms), interference (thin films), diffraction (slits), and polarization (sunglasses).

See Chapter 11: Light and Glossary: Light Waves.

What is electric charge?

Electric charge is a fundamental property of matter that causes it to experience electromagnetic force. Charge exists in two types: positive (protons carry positive charge) and negative (electrons carry negative charge). Like charges repel, opposite charges attract. Charge is quantized—it comes in discrete units equal to the electron charge (1.6 × 10⁻¹⁹ coulombs). The Law of Conservation of Charge states that the total electric charge in an isolated system remains constant. Charge can be transferred between objects through friction (rubbing), contact (touching), or induction (bringing charged objects near).

See Chapter 12: Electric Charge and Glossary: Electric Charge.

What is an electric field?

An electric field is a region around a charged object where other charged objects experience an electric force. The field is a vector quantity pointing in the direction a positive test charge would be pushed. Electric field strength equals force per unit charge (N/C) and is visualized using field lines—imaginary lines showing field direction and strength (closer lines = stronger field). Field lines radiate outward from positive charges and inward toward negative charges. Electric fields enable action-at-a-distance: charged objects don't need to touch to exert forces on each other.

See Chapter 12: Electric Field and Glossary: Electric Field.

Technical Detail Questions

What is the difference between precision and accuracy?

Precision refers to the reproducibility of measurements—how close repeated measurements are to each other—while accuracy refers to how close measurements are to the true or accepted value. You can have precise but inaccurate measurements (consistently measuring 9.2 m when the true value is 10.0 m) or accurate but imprecise measurements (measurements scatter around the true value: 9.8 m, 10.3 m, 9.9 m, 10.1 m). Ideal measurements are both precise (consistent) and accurate (correct). A poorly calibrated scale might give precise but inaccurate readings that cluster around the wrong value.

See Chapter 1: Precision vs Accuracy and Glossary: Precision vs Accuracy.

What are significant figures and why do they matter?

Significant figures are the digits in a measurement that carry meaningful information about its precision. They indicate the reliability of measured or calculated values. Rules: (1) all non-zero digits are significant, (2) zeros between non-zero digits are significant, (3) leading zeros are not significant, (4) trailing zeros after a decimal point are significant. Measuring 12.50 cm has four significant figures, indicating precision to the hundredths place. In calculations, your answer should have no more significant figures than the least precise measurement used. Significant figures prevent false precision—claiming accuracy you don't actually have.

See Chapter 1: Significant Figures and Glossary: Significant Figures.

What is dimensional analysis and how is it used?

Dimensional analysis is a mathematical technique using units of measurement to check equations and convert between different unit systems. It's based on the principle that valid equations must be dimensionally consistent—both sides must have the same units. To convert units, multiply by conversion factors equal to 1 (e.g., 1 m/100 cm, 60 s/1 min) arranged so unwanted units cancel. For example, converting 50 mi/h to m/s requires multiplying by (1609 m/1 mi) × (1 h/3600 s) = 22.4 m/s. Dimensional analysis catches calculation errors and ensures physical validity.

See Chapter 1: Dimensional Analysis and Glossary: Dimensional Analysis.

What is the difference between speed and velocity?

Speed is a scalar quantity measuring the rate of distance covered (distance ÷ time), while velocity is a vector quantity describing the rate of change of position (displacement ÷ time), including direction. A car traveling 100 km in 2 hours has a speed of 50 km/h, but we need direction to specify velocity (50 km/h northward). Average speed equals total distance divided by total time; average velocity equals net displacement divided by total time. If you drive in a circle and return to your starting point, your average velocity is zero (no net displacement) even though your average speed is nonzero.

See Glossary: Speed and Velocity.

What are kinematic equations and when can I use them?

Kinematic equations are four mathematical relationships connecting displacement, initial velocity, final velocity, acceleration, and time for uniformly accelerated motion (constant acceleration). The equations are: (1) v = v₀ + at, (2) x = x₀ + v₀t + ½at², (3) v² = v₀² + 2a(x - x₀), (4) x = x₀ + ½(v₀ + v)t. Use these equations only when acceleration is constant. They apply to free fall (constant a = g), projectile motion (constant vertical acceleration), and uniformly accelerated cars. They don't apply when acceleration changes, like a rocket with decreasing fuel mass or non-uniform circular motion.

See Chapter 2: Kinematic Equations and Glossary: Kinematic Equations.

What is projectile motion?

Projectile motion is two-dimensional motion of an object under the sole influence of gravity, combining horizontal uniform motion (constant velocity, zero acceleration) with vertical uniformly accelerated motion (constant downward acceleration g = 9.8 m/s²). The path is parabolic. To analyze projectile motion, decompose the initial velocity into horizontal and vertical components using trigonometry, then apply kinematic equations separately to each direction. Time is the linking variable—horizontal and vertical motions share the same time interval. Examples include thrown balls, kicked soccer balls, and cannonballs.

See Chapter 3: Projectile Motion and Glossary: Projectile Motion.

What is free fall?

Free fall is motion under the sole influence of gravity, where all objects accelerate downward at the same rate regardless of mass (assuming negligible air resistance). Near Earth's surface, this acceleration is approximately 9.8 m/s² downward. Galileo demonstrated that a feather and hammer dropped on the Moon (no air) fall at the same rate. On Earth, air resistance affects light objects more than heavy objects, causing apparent differences in fall rate. In free fall, only gravity acts—no normal force, no air resistance. Astronauts in orbit experience continuous free fall around Earth.

See Chapter 2: Free Fall and Glossary: Free Fall.

What is centripetal force?

Centripetal force is the net force directed toward the center of a circular path that causes an object to follow that curved trajectory rather than moving in a straight line. It's not a new type of force—it's the net result of real forces like tension, gravity, or friction acting toward the center. For circular motion at constant speed, centripetal force equals mv²/r, where m is mass, v is speed, and r is radius. When you swing a ball on a string, the string's tension provides centripetal force. For a car turning, friction between tires and road provides centripetal force.

See Chapter 5: Centripetal Force and Glossary: Centripetal Force.

What is the Work-Energy Theorem?

The Work-Energy Theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² - ½mv₀². This powerful relationship connects force (through work) directly to motion (kinetic energy). When you apply brakes to a car, the negative work done by friction reduces the car's kinetic energy to zero. The theorem applies to both constant and variable forces and provides an alternative to Newton's Second Law for solving mechanics problems. It's particularly useful when forces vary with position rather than time.

See Chapter 6: Work-Energy Theorem and Glossary: Work-Energy Theorem.

What is conservation of mechanical energy?

Conservation of mechanical energy states that in the absence of non-conservative forces (like friction), the total mechanical energy (sum of kinetic and potential energy) remains constant. As a pendulum swings, it continuously exchanges energy between kinetic (maximum at bottom) and potential (maximum at top), but the total stays constant. This principle applies when only conservative forces (gravity, springs) do work. With non-conservative forces present, mechanical energy decreases (converting to heat, sound, deformation) but total energy including all forms remains conserved according to the broader Law of Conservation of Energy.

See Chapter 6: Conservation of Energy and Glossary: Conservation of Energy.

What is impulse and how does it relate to momentum?

Impulse is the product of force and the time interval over which it acts, equal to the change in momentum: J = FΔt = Δp. Measured in N·s or kg·m/s, impulse describes how forces change an object's motion over time. The Impulse-Momentum Theorem states that impulse equals momentum change. This explains why airbags save lives: they increase collision time, reducing the force of impulse on passengers (same momentum change, longer time, therefore smaller force). Catching a baseball with a glove demonstrates this—you pull your hand back to increase stopping time and reduce impact force.

See Chapter 7: Impulse and Glossary: Impulse, Impulse-Momentum Theorem.

What is rotational inertia?

Rotational inertia (also called moment of inertia) is the resistance of a rotating object to changes in its rotational motion, depending on both mass and mass distribution relative to the rotation axis. Unlike linear inertia (just mass), rotational inertia increases when mass is farther from the axis: I = Σmr². A figure skater has less rotational inertia with arms pulled in (mass closer to axis) than with arms extended (mass farther from axis), explaining why pulling in arms increases spin rate (conservation of angular momentum). Rotational inertia is the rotational analog of mass in Newton's Second Law: τ = Iα.

See Chapter 8: Rotational Inertia and Glossary: Rotational Inertia.

What is angular momentum and how is it conserved?

Angular momentum is the rotational analog of linear momentum, calculated as the product of rotational inertia and angular velocity: L = Iω. Like linear momentum, angular momentum is conserved in isolated systems (no external torques). A spinning ice skater pulling in their arms demonstrates conservation—as I decreases (mass closer to axis), ω increases (spins faster) to keep L = Iω constant. Earth's rotation produces enormous angular momentum that stays constant, explaining why Earth continues spinning. Conservation of angular momentum explains everything from figure skating spins to formation of galaxies.

See Chapter 8: Angular Momentum and Glossary: Angular Momentum, Conservation of Angular Momentum.

What is Hooke's Law?

Hooke's Law states that the restoring force in a spring is directly proportional to its displacement from equilibrium: F = -kx, where k is the spring constant (stiffness) measured in N/m, and x is displacement. The negative sign indicates the force opposes displacement (pushes back toward equilibrium). A stiffer spring has a larger k value. Stretching a spring 5 cm requires twice the force needed to stretch it 2.5 cm. Hooke's Law applies to elastic materials within their elastic limit—beyond this, permanent deformation occurs and Hooke's Law fails. Springs following Hooke's Law produce simple harmonic motion.

See Chapter 9: Hooke's Law and Glossary: Hooke's Law.

What is resonance?

Resonance is the dramatic increase in amplitude when a system is driven at its natural frequency—the frequency at which it naturally oscillates. Every system has one or more natural frequencies determined by its physical properties (mass, stiffness, length). When external driving force matches the natural frequency, energy efficiently transfers to the system, building large oscillations. Examples include pushing a child on a swing at just the right timing, shattering wine glasses with sound at their resonant frequency, and the Tacoma Narrows Bridge collapse. Resonance can be useful (musical instruments) or destructive (structural failures).

See Chapter 9: Resonance and Glossary: Resonance.

What is wave interference?

Wave interference is the combination of two or more waves occupying the same space, producing a resultant wave according to the Superposition Principle—the resultant displacement equals the sum of individual wave displacements. Constructive interference occurs when waves combine in phase (crests align), producing larger amplitude. Destructive interference occurs when waves combine out of phase (crest meets trough), reducing or canceling amplitude. When two stones are dropped in water, ripples create complex patterns of constructive and destructive interference. Noise-canceling headphones use destructive interference to reduce unwanted sounds.

See Chapter 10: Wave Interference and Glossary: Wave Interference, Constructive Interference, Destructive Interference.

What is the Doppler Effect?

The Doppler Effect is the change in observed frequency of a wave when there is relative motion between the source and observer. When a source moves toward you (or you move toward it), you observe higher frequency (shorter wavelength); when moving apart, you observe lower frequency (longer wavelength). A train whistle sounds higher pitched as it approaches and lower pitched as it recedes. The Doppler Effect applies to all waves—sound, light, water. Police radar guns use the Doppler Effect to measure vehicle speeds. Astronomers use it to determine if stars are moving toward or away from Earth (redshift/blueshift).

See Chapter 10: Doppler Effect and Glossary: Doppler Effect.

What is refraction and why does it occur?

Refraction is the bending of waves as they pass from one medium to another due to a change in wave speed. Light slows down when entering denser media (air to glass) and speeds up when entering less dense media (water to air). Snell's Law quantifies refraction: n₁sin(θ₁) = n₂sin(θ₂), where n is the index of refraction (ratio of light speed in vacuum to light speed in medium). Refraction explains why a straw appears bent in water, why lenses focus light, and why objects underwater appear closer than they are. The amount of bending depends on the ratio of speeds in the two media.

See Chapter 11: Refraction and Glossary: Refraction, Snell's Law.

What is total internal reflection?

Total internal reflection is the complete reflection of light at the boundary between a denser and less dense medium when the angle of incidence exceeds the critical angle. Beyond the critical angle, no light refracts into the second medium—all light reflects back. This occurs only when light travels from higher to lower refractive index (e.g., glass to air, water to air, but not air to glass). Fiber optic cables exploit total internal reflection to trap light inside, enabling high-speed data transmission over long distances. Diamonds sparkle brilliantly because their high refractive index causes extensive total internal reflection, trapping and reflecting light internally.

See Chapter 11: Total Internal Reflection and Glossary: Total Internal Reflection.

What is Coulomb's Law?

Coulomb's Law describes the electric force between two charged objects as directly proportional to the product of their charges and inversely proportional to the square of the distance between them: F = k(q₁q₂)/r², where k = 8.99 × 10⁹ N·m²/C² is Coulomb's constant. Like charges repel (positive force), opposite charges attract (negative force). The force follows an inverse square law like gravity—doubling the distance reduces the force to one-fourth. Coulomb's Law applies to point charges or spherically symmetric charge distributions and is fundamental to understanding electric interactions.

See Chapter 12: Coulomb's Law and Glossary: Coulomb's Law.

Common Challenges

Why do heavier and lighter objects fall at the same rate?

This counterintuitive result follows from Newton's Second Law and the universal nature of gravitational acceleration. While heavier objects experience more gravitational force (F = mg), they also have more inertia (resistance to acceleration). The greater force and greater inertia exactly cancel: a = F/m = mg/m = g. All objects near Earth's surface accelerate downward at g = 9.8 m/s² regardless of mass. Air resistance obscures this in everyday experience—light objects like feathers have high surface area relative to weight, causing significant air drag. In vacuum (as demonstrated on the Moon), a feather and hammer fall together.

See Chapter 2: Free Fall and Glossary: Free Fall.

How do I know which kinematic equation to use?

Choose based on which variables you know and which you're solving for. Each equation uses four of five kinematic variables (displacement, initial velocity, final velocity, acceleration, time): (1) v = v₀ + at (no displacement), (2) x = x₀ + v₀t + ½at² (no final velocity), (3) v² = v₀² + 2a(x - x₀) (no time), (4) x = x₀ + ½(v₀ + v)t (no acceleration). List known variables, identify what you're solving for, and select the equation containing those variables. Sometimes you'll need to use multiple equations sequentially. Always check that acceleration is constant before using kinematic equations.

See Chapter 2: Kinematic Equations and Glossary: Kinematic Equations.

What's the difference between mass and weight?

Mass is the amount of matter in an object (measured in kilograms), an intrinsic property that doesn't change with location. Weight is the gravitational force acting on that mass (measured in newtons), calculated as W = mg where g is local gravitational acceleration. Your mass remains 70 kg whether on Earth, Moon, or in space. Your weight on Earth is 686 N (70 kg × 9.8 m/s²), on the Moon is 115 N (70 kg × 1.6 m/s²), and in deep space is nearly zero. Weight depends on location; mass doesn't. Bathroom scales actually measure weight but display mass.

See Chapter 4: Mass vs Weight and Glossary: Mass vs Weight.

Why doesn't an object in equilibrium move?

An object in equilibrium experiences zero net force—all forces are balanced. Newton's First Law states that zero net force means zero acceleration, not necessarily zero velocity. Static equilibrium means the object remains at rest (zero velocity). Dynamic equilibrium means the object moves with constant velocity (zero acceleration but nonzero velocity). A book resting on a table is in static equilibrium (normal force balances weight). A parachutist falling at terminal velocity is in dynamic equilibrium (air resistance balances weight). In both cases, net force equals zero, so acceleration equals zero.

See Chapter 4: Equilibrium and Glossary: Equilibrium, Static Equilibrium, Dynamic Equilibrium.

How can work be zero if I'm pushing hard?

Work requires displacement in the direction of force. If you push against a wall that doesn't move, you do zero work despite expending energy (which converts to heat in your muscles). Work equals force times displacement times cos(θ): W = F·d·cos(θ). Three scenarios produce zero work: (1) zero displacement (pushing an immovable wall), (2) force perpendicular to displacement (θ = 90°, like centripetal force in circular motion), or (3) force opposite to displacement (negative work, like friction slowing a sliding block). "Work" in physics has a precise technical meaning different from everyday usage of the word.

See Chapter 6: Work and Glossary: Work.

Why is kinetic friction less than static friction?

When surfaces are at rest relative to each other, microscopic irregularities interlock more deeply, creating stronger bonds between surfaces. Once motion begins, surfaces ride over these irregularities rather than settling into them, reducing the friction force. The coefficient of kinetic friction (μₖ) is typically 20-40% smaller than the coefficient of static friction (μₛ) for the same material pair. This explains why it's harder to start pushing a heavy box than to keep it moving, and why anti-lock brakes work—preventing wheel lockup keeps you in kinetic rather than static friction regime, allowing steering control.

See Chapter 5: Friction and Glossary: Static Friction, Kinetic Friction.

How do I set up free body diagrams?

Free body diagrams isolate a single object and show all forces acting on it. Follow these steps: (1) Choose your object and draw it as a simple shape or dot, (2) Identify all forces acting ON the object (not forces BY the object), (3) Draw force vectors as arrows starting from the object's center, with length proportional to magnitude and direction showing force direction, (4) Label each force (weight, normal, tension, friction, etc.), (5) Choose coordinate axes aligned with motion or slopes. Don't include forces the object exerts on other things—only forces acting on your chosen object. Free body diagrams are essential for applying Newton's Second Law.

See Chapter 4: Forces and Newton's Laws.

Why does a satellite in orbit not fall to Earth?

A satellite in orbit IS falling toward Earth continuously—it's in free fall! The key is that it has sufficient tangential velocity that as it falls, Earth's curved surface falls away beneath it at the same rate. The satellite's path curves downward due to gravity at exactly the rate Earth's surface curves away, resulting in a circular (or elliptical) orbit. The satellite needs no fuel to maintain orbit—once in motion, it continues indefinitely in the absence of air resistance. If you could throw a baseball fast enough (about 7.9 km/s horizontally), it would orbit Earth. Lower orbital velocity means tighter curves and eventual atmospheric reentry.

See Chapter 5: Centripetal Force and Glossary: Centripetal Force.

What happens to energy in inelastic collisions?

In inelastic collisions, kinetic energy decreases (converts to other forms) while momentum remains conserved. The "lost" kinetic energy doesn't disappear—it transforms into heat, sound, permanent deformation, and vibrational energy. Car crashes dramatically demonstrate this: crumpling metal, screeching sounds, and heat from friction all represent kinetic energy conversion. Perfectly inelastic collisions (objects stick together) lose maximum kinetic energy consistent with momentum conservation. Even though kinetic energy isn't conserved in inelastic collisions, total energy including all forms remains conserved according to the Law of Conservation of Energy.

See Chapter 7: Collisions and Glossary: Inelastic Collisions.

Why does a spinning figure skater speed up when pulling arms in?

This demonstrates conservation of angular momentum: L = Iω must remain constant in the absence of external torques. When the skater pulls arms inward, rotational inertia I decreases (mass moves closer to rotation axis). To keep L = Iω constant, angular velocity ω must increase proportionally. If I drops to half its original value, ω doubles. The skater does work pulling arms in against centrifugal tendency, converting chemical energy to increased rotational kinetic energy (½Iω²). Despite increased kinetic energy, angular momentum stays constant. This same principle explains why planets orbit faster when closer to the sun.

See Chapter 8: Conservation of Angular Momentum and Glossary: Conservation of Angular Momentum.

Best Practices

How should I approach physics problem-solving?

Use the GUPSP framework: Given (list known quantities with units), Unknown (identify what you're solving for), Principle (state relevant physics laws and equations), Solve (perform calculations step-by-step, showing work), Ponder (check reasonableness of answer: correct units? Sensible magnitude? Limiting cases?). Draw diagrams for all problems—free body diagrams for forces, motion diagrams for kinematics, energy bar charts for energy problems. Write equations symbolically before substituting numbers. Always include units and check dimensional consistency. If stuck, ask: What physics principles apply? What's the strategy? Can I solve simpler versions first?

See Course Description: Problem-Solving Framework.

When should I use energy methods versus force methods?

Use energy methods (work-energy theorem, conservation of energy) when: (1) you know positions and speeds but not detailed time information, (2) forces vary with position, (3) multiple forces act and you care about overall effect, or (4) the problem involves springs or gravitational potential energy. Use force methods (Newton's Second Law) when: (1) you need to find acceleration or forces at specific instants, (2) you need time-dependent information, (3) forces are constant or easily described as functions of time. Many problems can be solved either way—choose the approach that requires fewer steps.

See Chapter 6: Work and Energy.

How do I know which forces to include in my free body diagram?

Include only forces that directly act ON the object you're analyzing, not forces BY the object on other things. Common forces: Weight (gravity, always downward with magnitude mg), Normal force (perpendicular contact force from surfaces), Tension (pulling force through ropes/strings/cables), Friction (parallel to surfaces, opposes relative motion), Applied forces (pushes/pulls you explicitly apply), Spring forces (following Hooke's Law), Drag (air/fluid resistance, opposite to velocity). Don't include internal forces, centripetal force (it's a net effect of other forces), or inertial "forces" (ma is not a force—it's the result of forces).

See Chapter 4: Forces.

What's the best way to work with vectors?

For vector problems, use the component method: (1) Draw a coordinate system aligned with the problem (often with x horizontal and y vertical, or x along slopes), (2) Decompose all vectors into components using trigonometry: Aₓ = A cos(θ), Aᵧ = A sin(θ), (3) Work with components separately—x-components don't affect y-components, (4) Add/subtract corresponding components, (5) If needed, reconstruct magnitude using Pythagorean theorem (A = √(Aₓ² + Aᵧ²)) and direction using inverse tangent (θ = tan⁻¹(Aᵧ/Aₓ)). For 3D problems, include z-components. Never add magnitudes of non-parallel vectors directly—always use components or graphical methods.

See Chapter 1: Vectors and Vector Operations.

How do I analyze projectile motion problems?

Separate horizontal and vertical motions—they're independent except for sharing the same time. Horizontal: constant velocity (vₓ = v₀ cos(θ₀)), zero acceleration, use x = x₀ + vₓt. Vertical: uniformly accelerated motion with a = -g = -9.8 m/s², use kinematic equations with initial vertical velocity vᵧ₀ = v₀ sin(θ₀). Time is the linking variable connecting horizontal and vertical motions. Solve for time using one direction, then use that time in the other direction. Draw a trajectory diagram showing key points: launch, peak (vᵧ = 0), landing. Maximum range at 45° launch angle (neglecting air resistance).

See Chapter 3: Projectile Motion and Glossary: Projectile Motion.

What's the best way to prepare for laboratory work?

Before lab: (1) Read the procedure completely, (2) Identify the physics concepts being investigated, (3) Understand what measurements you'll make and why, (4) Predict qualitative results, (5) Review safety protocols. During lab: (1) Record data directly in your notebook—no loose papers, (2) Include units with every measurement, (3) Note unusual observations, (4) Repeat measurements for reliability, (5) Estimate uncertainties. After lab: (1) Graph data promptly while details are fresh, (2) Calculate uncertainties and propagate through calculations, (3) Compare results to predictions/theory, (4) Identify sources of error, (5) Discuss what you learned beyond "confirming" expected results.

See Course Description: Laboratory Work.

How should I use the MicroSims effectively?

MicroSims are most valuable when used actively, not passively. Before using a MicroSim: read the related textbook section to understand the concept. During exploration: (1) Start with default parameters to see normal behavior, (2) Vary ONE parameter at a time to isolate effects, (3) Make predictions before changing parameters ("What will happen if...?"), (4) Test extreme values to find boundaries, (5) Look for patterns and relationships between variables. After exploration: (1) Summarize what you learned in words, (2) Connect simulation behavior to equations, (3) Think about real-world examples, (4) Try related problems to reinforce understanding. MicroSims supplement, not replace, hands-on laboratory experience.

See MicroSims Index.

What resources should I use when I'm stuck?

Try resources in this order: (1) Reread the relevant textbook section carefully, (2) Check the glossary for term definitions, (3) Review worked examples similar to your problem, (4) Use MicroSims to visualize the concept, (5) Consult the learning graph to ensure you understand prerequisites, (6) Form a study group to discuss with peers, (7) Visit office hours or tutoring sessions with specific questions prepared. When asking for help, show your work—explain what you've tried and where you're stuck. Avoid just looking up answers—struggling productively builds problem-solving skills. Use online resources (Khan Academy, PhET simulations, HyperPhysics) as supplements, not replacements, for the textbook.

How should I study for physics exams?

Physics isn't memorization—it's understanding and application. Study strategies: (1) Active practice: Solve problems without looking at solutions, (2) Concept review: Explain concepts in your own words without referring to notes, (3) Problem categorization: Group problems by concept/technique rather than chapter, (4) Mistake analysis: Review incorrect homework/quiz problems to identify patterns in your errors, (5) Formula derivation: Derive key equations from fundamentals rather than memorizing, (6) Limiting cases: Check equations for extreme values (What happens when v→0? when m→∞?). Create summary sheets connecting concepts. Form study groups for discussion. Prioritize understanding over memorization.

Advanced Topics

How does conservation of energy relate to conservation of momentum?

Both are fundamental conservation laws but apply in different contexts. Conservation of momentum requires no net external force and is a vector law (conserved in each direction independently). Conservation of energy (total energy including all forms) always holds, but conservation of mechanical energy requires no non-conservative forces. These laws are independent—they provide different constraints on physical systems. In elastic collisions, both momentum and kinetic energy are conserved, giving you two equations to solve for two unknowns. In inelastic collisions, momentum is conserved but kinetic energy isn't, reflecting energy transformation to other forms.

See Chapter 6: Energy and Chapter 7: Momentum.

What is the relationship between torque and angular acceleration?

Torque causes angular acceleration just as force causes linear acceleration. Newton's Second Law for rotation is τ_net = Iα, where τ is net torque, I is rotational inertia, and α is angular acceleration. This is directly analogous to F_net = ma. Greater torque produces greater angular acceleration; greater rotational inertia produces less angular acceleration for given torque. Just as force is the time derivative of linear momentum (F = dp/dt), torque is the time derivative of angular momentum (τ = dL/dt). When net torque equals zero, angular momentum is conserved—the rotational equivalent of momentum conservation.

See Chapter 8: Torque and Rotation.

How do standing waves form?

Standing waves form through interference of two identical waves traveling in opposite directions, typically from a wave reflecting back on itself. At specific frequencies (determined by boundary conditions and medium properties), the incident and reflected waves interfere constructively and destructively at fixed positions, creating a pattern that appears stationary. Nodes (points of zero amplitude) occur where waves destructively interfere continuously; antinodes (points of maximum amplitude) occur where waves constructively interfere continuously. Musical instruments produce standing waves: guitar strings vibrate in patterns with nodes at both fixed ends, determining possible frequencies (harmonics).

See Chapter 10: Standing Waves and Glossary: Standing Waves.

What causes dispersion of light through a prism?

Dispersion—the separation of white light into its component colors—occurs because the refractive index of materials depends on wavelength. In glass, blue light (shorter wavelength) travels slower and refracts more than red light (longer wavelength). When white light enters a prism at an angle, different wavelengths refract by different amounts, separating spatially into a spectrum. The same phenomenon creates rainbows: water droplets act as prisms, dispersing sunlight. Dispersion limits optical system performance in telescopes and cameras, requiring special corrective lenses. It also enables spectroscopy—analyzing light composition by separating wavelengths.

See Chapter 11: Dispersion and Glossary: Dispersion.

How do lenses form images?

Lenses refract light rays to converge (convex/converging lenses) or diverge (concave/diverging lenses). Convex lenses bring parallel rays to a focal point, creating real images (can be projected on screen) when objects are beyond focal length, or virtual images (magnified, like magnifying glass) when objects are closer than focal length. Concave lenses spread parallel rays as if coming from a focal point, always creating virtual images that are reduced. The lens equation (1/f = 1/dₒ + 1/dᵢ) relates focal length f, object distance dₒ, and image distance dᵢ. Ray diagrams graphically show image formation by tracing key rays through lenses.

See Chapter 11: Lenses and Glossary: Lenses, Convex Lenses, Concave Lenses.

What is the relationship between electric potential and electric field?

Electric field and electric potential are intimately related: the electric field is the negative gradient (spatial rate of change) of electric potential. In one dimension: E = -dV/dx. Electric potential (measured in volts) represents potential energy per unit charge, while electric field (measured in V/m or N/C) represents force per unit charge. Field points in the direction of decreasing potential—from high potential to low potential. You can calculate potential from field: V = -∫E·dx. When moving a positive charge against the electric field, you increase its potential energy. Equipotential surfaces are always perpendicular to electric field lines.

See Chapter 12: Electric Potential and Glossary: Electric Potential, Electric Field.

How can I extend my learning beyond this textbook?

Explore advanced topics through: (1) Online resources: MIT OpenCourseWare, Khan Academy, PhET Interactive Simulations, Walter Lewin's lectures, (2) Books: "The Feynman Lectures on Physics" for intuitive explanations, "University Physics" for depth, "Six Easy Pieces" for conceptual understanding, (3) Laboratory: Design your own experiments investigating questions that interest you, (4) Competitions: Physics Olympiad, Science Olympiad, Science Fair, (5) Research: Email local university professors about research opportunities, (6) Technology: Build Arduino/Raspberry Pi physics projects, program simulations. Focus on deep understanding over broad coverage—mastering fundamentals enables self-directed advanced study.

What physics concepts connect to engineering and technology?

Nearly all engineering relies on physics principles: Mechanical engineering applies mechanics (forces, energy, materials); Electrical engineering builds on electricity and magnetism; Civil engineering uses statics and dynamics for structures; Aerospace engineering applies fluid dynamics and thermodynamics; Computer engineering depends on solid-state physics and electromagnetism; Biomedical engineering combines mechanics with electromagnetic imaging; Chemical engineering uses thermodynamics and transport phenomena. Understanding physics fundamentals is essential for engineering innovation. Many technologies you use daily—smartphones, GPS, MRI scanners, solar panels, LED lights—are direct applications of physics concepts you're learning.

How do physicists handle problems where multiple principles apply?

Complex problems often require combining multiple physics principles strategically. General approach: (1) Identify relevant principles (conservation laws, Newton's Laws, energy methods, etc.), (2) Choose the most efficient approach based on what's known and unknown, (3) Apply principles systematically, using each to extract different information, (4) Use one result to inform the next step. Example: A pendulum problem might use conservation of energy to find speed at bottom, then Newton's Second Law to find tension in string at that point. Strategy: Conservation laws provide global constraints (useful when you don't know details). Force laws give local/instantaneous information. Symmetry often simplifies problems dramatically.