Simple vs. Physical Pendulum Comparison
About This Diagram
This side-by-side comparison illustrates the key differences between a simple pendulum (idealized point mass on a massless string) and a physical pendulum (real rigid body with distributed mass).
Simple Pendulum
- Model: Point mass on a massless, inextensible string
- Center of mass: Located at the bob
- Period formula: T = 2π√(L/g)
- Key parameter: Length L from pivot to mass
Physical Pendulum
- Model: Rigid body that can rotate about a fixed axis
- Center of mass: Located within the body (may not be at the end)
- Period formula: T = 2π√(I/mgd)
- Key parameters: Moment of inertia I, distance d from pivot to center of mass
Key Differences
| Property | Simple Pendulum | Physical Pendulum |
|---|---|---|
| Mass distribution | All at one point | Distributed throughout body |
| String/rod | Massless string | Rigid body with mass |
| Formula | T = 2π√(L/g) | T = 2π√(I/mgd) |
| Examples | Idealized model | Swinging door, meter stick |
Lesson Plan
Discussion Questions
- Why doesn't mass appear in the simple pendulum formula?
- Under what conditions does a physical pendulum become equivalent to a simple pendulum?
- Would a uniform rod pivoted at its end have a longer or shorter period than a simple pendulum of the same length?