AP Physics C: Mechanics Review Guide

AP Physics C: Mechanics is AP Physics 1 rewritten in calculus. The same topics appear (kinematics, forces, energy, momentum, rotation, gravitation, oscillations), but you use derivatives and integrals to solve them instead of algebra.

Exam structure

• 3 hours 15 minutes total.
• Section I: 35 multiple choice (1 hour 15 minutes, split into no-calc 20 questions and calc 15 questions).
• Section II: 3 free response (1 hour 45 minutes, split no-calc and calc).
• Sections equally weighted (50-50).

Key differences from Physics 1

Calculus notation

• Velocity is the derivative: v equals dx slash dt.
• Acceleration is the derivative: a equals dv slash dt.
• Position from acceleration uses integration: x equals the integral of v dt.
• Work equals integral of force: W equals the integral of F dot dx.
• Impulse equals integral of force: J equals the integral of F dt.

Unit 1: Kinematics

If acceleration is constant: v equals v0 plus at, x equals x0 plus v0 t plus (one-half) a t squared. If a(t) is given, integrate directly.

Unit 2: Newton's Laws

F equals ma (where a is d squared x slash dt squared). Set up force equation and integrate to find motion.

Unit 3: Work and Energy

W equals integral of F dx. Power equals dW slash dt equals F times v.

Unit 4: Momentum and Impulse

J equals integral of F dt equals change in p. In isolated systems, total momentum is conserved.

Unit 5: Rotation

Omega equals d theta slash dt. Alpha equals d omega slash dt. Tau equals I times alpha (rotational version of F equals m a).

Unit 6: Gravitation

F equals G M m slash r squared. For circular orbit: v equals square root (G M slash r). Escape velocity: v equals square root (2 G M slash r).

Unit 7: Oscillations

SHM: d squared x slash dt squared equals minus (k slash m) x. Solution: x(t) equals A cos(omega t plus phi). Energy oscillates between kinetic and potential.

How to score a 5

1. Understand the relationship between x, v, a. Know when to differentiate and integrate.
2. Master setting up F equals ma from free-body diagrams.
3. Use energy methods when forces are complicated. Energy conservation is often easier than Newton's second law.
4. Know the three big moments of inertia: solid cylinder I equals (one-half) m r squared, hollow cylinder I equals m r squared, solid sphere I equals (two-fifths) m r squared.
5. For oscillations, recognize SHM (pendulum, spring) and that period depends on system properties, not amplitude.