College Board-Aligned Original Notes

AP Physics C: Mechanics Unit 7 Topic 3: Physical pendulums

A physical pendulum is an extended rigid body oscillating about a pivot, so rotational inertia matters.

Unit 7: Oscillations. College Board exam weighting listed for this unit: 10%-15% of multiple-choice score.

What to Know

The restoring torque comes from gravity acting at the center of mass.
The period depends on rotational inertia, mass, gravity, and distance from pivot to center of mass.
The parallel-axis theorem is often needed when the pivot is not through the center of mass.
Always connect this topic back to the larger unit: Oscillations.

Detailed Notes

Physical pendulums belongs to Unit 7: Oscillations. A physical pendulum is an extended rigid body oscillating about a pivot, so rotational inertia matters. In AP Physics C: Mechanics, the explanation should connect diagrams, calculus relationships, and the physical meaning of each quantity.

Key relationships: The restoring torque comes from gravity acting at the center of mass. The period depends on rotational inertia, mass, gravity, and distance from pivot to center of mass. The parallel-axis theorem is often needed when the pivot is not through the center of mass.

Model to use: Mark the pivot, center of mass, gravitational force, lever arm, and rotational inertia about the pivot. Define the coordinate system, system boundary, and sign convention before writing equations.

AP-style move: For extended bodies, avoid using the simple-pendulum formula unless the object can be modeled as a point mass. Show the setup symbolically, then interpret the answer with units and direction when relevant.

Key Vocabulary

Physical pendulum

An extended rigid body that oscillates about a pivot.

Center-of-mass lever arm

Distance from pivot to the center of mass used for gravitational torque.

Pivot-axis inertia

Rotational inertia calculated about the actual pivot.

Parallel-axis theorem

A theorem relating rotational inertia about parallel axes.

Rigid-body oscillator

An extended object oscillating as a single rigid body.

Quick Practice

How would you explain Physical pendulums in one or two AP-style sentences?

Name the concept, apply it to a specific example or source, and explain the reasoning that connects the evidence to your answer.

Official Alignment

Reference and Attribution

AP Physics C: Mechanics concept reference: AP Physics C Mechanics-Concise Summary Notes by IITian Academy. EduCompanion used this source as a topic checklist and conceptual reference, then rewrote the study notes in original wording.

AP Physics C Mechanics-Concise Summary Notes