Quiz: Rotational Motion and Angular Momentum
Test your understanding of rotational motion and angular momentum with these 10 questions.
1. What is angular displacement?
- The distance traveled along an arc
- The change in rotational position measured in radians
- The speed of rotation
- The force required to rotate an object
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The correct answer is B. Angular displacement (θ) measures the change in rotational position. It's typically measured in radians (rad), where 2π radians = 360° = 1 complete rotation. Unlike linear displacement, angular displacement is the same for all points on a rigid rotating body, regardless of distance from the axis.
Concept Tested: Angular Displacement
2. How is angular velocity related to tangential velocity?
- They are always equal
- Tangential velocity equals angular velocity times radius: v = ωr
- Angular velocity is the square root of tangential velocity
- They have no mathematical relationship
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The correct answer is B. For an object rotating about an axis, the tangential velocity (linear speed of a point) depends on both the angular velocity (ω) and the distance from the axis (r): v = ωr. Points farther from the axis move faster, even though all points have the same angular velocity.
Concept Tested: Angular Velocity
3. What is torque?
- The rate of change of position
- A rotational force that causes angular acceleration
- The total energy of a rotating object
- The resistance to any type of motion
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The correct answer is B. Torque (τ) is the rotational equivalent of force. It's the product of force and the perpendicular distance from the axis: τ = r⊥F. Torque causes angular acceleration, just as force causes linear acceleration. It depends on both the magnitude of the force and how far from the axis it's applied.
Concept Tested: Torque
4. You push on a door handle 0.8 m from the door's hinge with a force of 25 N perpendicular to the door. What is the torque about the hinge?
- 20 N·m
- 25 N·m
- 31.25 N·m
- 0.032 N·m
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The correct answer is A. Torque = r⊥ × F = 0.8 m × 25 N = 20 N·m. This is the rotational effect that will cause the door to accelerate rotationally (open). The farther from the hinge you apply force, or the larger the force, the greater the torque.
Concept Tested: Torque
5. What is rotational inertia?
- The resistance to change in rotational motion
- The mass of a rotating object
- The kinetic energy of rotation
- The angular velocity of an object
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The correct answer is A. Rotational inertia (I) is an object's resistance to angular acceleration, analogous to mass in linear motion. It depends on both the object's mass and how that mass is distributed relative to the axis of rotation. Objects with mass farther from the axis have greater rotational inertia.
Concept Tested: Rotational Inertia
6. How does an ice skater spinning with arms extended change their spin rate when pulling arms inward?
- Spin rate decreases due to increased friction
- Spin rate increases because rotational inertia decreases
- Spin rate remains constant by conservation of angular momentum
- Spin rate decreases because tension in the arms resists rotation
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The correct answer is B. By conservation of angular momentum (L = Iω), if I decreases (arms pulled in), ω must increase to keep L constant. The skater spins faster. This is a dramatic demonstration of angular momentum conservation without any external torques.
Concept Tested: Conservation of Angular Momentum
7. A disk rotates at 2 rad/s and has a rotational inertia of 3 kg·m². What is its rotational kinetic energy?
- 3 J
- 6 J
- 12 J
- 1.5 J
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The correct answer is B. Rotational kinetic energy is KE_rot = ½Iω². KE_rot = ½(3 kg·m²)(2 rad/s)² = ½(3)(4) = 6 J. This is the rotational analog of linear kinetic energy (½mv²).
Concept Tested: Rotational Kinetic Energy
8. What is angular momentum?
- The torque applied to an object
- The product of rotational inertia and angular velocity
- The force times distance
- The rate of change of torque
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The correct answer is B. Angular momentum (L) is the rotational analog of linear momentum: L = Iω. It measures the 'quantity of rotational motion.' Like linear momentum, angular momentum is conserved in systems with no external torque.
Concept Tested: Angular Momentum
9. A wheel rolling without slipping down a ramp will reach the bottom sooner than a sliding block of the same mass. Why?
- The wheel is lighter than the block
- The wheel converts some potential energy to rotational kinetic energy, while the block converts all to linear kinetic energy
- Friction accelerates the wheel but decelerates the block
- The wheel's shape makes it roll faster
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The correct answer is C. Actually, the block reaches the bottom first, not the wheel. The block slides without friction loss, converting all PE to KE of translation. The wheel must share energy between translational and rotational motion, so less goes to translation. Friction on the wheel provides torque but doesn't remove energy from the system if there's no slipping.
Concept Tested: Rolling Motion
10. When a torque is applied to a rigid object, what changes in the object's motion?
- Its linear velocity
- Its angular velocity or its axis of rotation
- Its mass
- Its color or appearance
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The correct answer is B. Torque causes angular acceleration (τ = Iα), which changes the angular velocity. For a fixed axis, this changes how fast the object spins. Torque can also change the orientation of the rotation axis itself (as in precession). Torque does not directly change linear velocity or mass.
Concept Tested: Angular Acceleration