AP Physics C: Mechanics

Advanced Placement Physics C: Mechanics with calculus-based physics principles.

Advanced Topics

Rotational Dynamics and Torque

Spinning Motion and Forces

Not all motion is in straight lines—many objects rotate! Rotational dynamics links angular motion to forces.

Angular Quantities

  • Angular displacement (\( \theta \))
  • Angular velocity (\( \omega \))
  • Angular acceleration (\( \alpha \))

Torque

Torque is the rotational equivalent of force: \( \tau = r \times F \). It causes objects to spin or change how fast they spin.

Rotational Inertia

The distribution of mass affects how hard it is to rotate an object. The further the mass is from the axis, the more torque is needed.

Applications

  • Gears in a bicycle
  • Turning a wrench

Torque and rotational inertia explain why figure skaters spin faster when they pull their arms in.

Key Formula

\[\tau = r \times F\]

Examples

  • A seesaw balances when torques on each side are equal.

  • A spinning top slows down due to frictional torque.

In a Nutshell

Rotational dynamics explains how forces cause objects to spin and how mass distribution affects rotation.

Key Terms

Torque
A measure of the force causing an object to rotate.
Moment of Inertia
A measure of how mass is distributed relative to an axis of rotation.