AP Physics C: Mechanics (College Board): complete calculus-based guide to the units, the science practices and the exam

College Board AP Physics C: Mechanics is the calculus-based mechanics course, designed to be the equivalent of a first-semester, calculus-based introductory college physics course for students heading into the physical sciences or engineering. Where the algebra-based AP Physics 1 uses proportional reasoning, AP Physics C uses derivatives and integrals directly: velocity and acceleration are derivatives of position, work and impulse are integrals, the center of mass and the moment of inertia are found by integration, and resistive forces and oscillations lead to differential equations. This page is the index: below is a map of the seven units, the exam structure, and how to study each one. This library covers all seven units in full.

The AP Physics C Mechanics units

The College Board organizes the content into seven units, each carrying an exam weighting (the share of questions it tends to contribute). The framework was revised for 2024-25, aligning the unit titles and language with the other AP Physics courses while keeping the calculus-based depth.

Unit 1 Kinematics (10 to 15%)

Scalars and vectors, velocity and acceleration as derivatives of position, recovering motion by integration, representing motion with graphs (slopes and areas), reference frames and relative motion, and vectors and motion in two dimensions including projectile motion.

Unit 2 Force and Translational Dynamics (20 to 25%)

Systems and the center of mass (by integration), forces and free-body diagrams, Newton's three laws, the gravitational force and field (including inside a sphere), kinetic and static friction, spring forces, velocity-dependent resistive forces with terminal velocity, and circular motion.

Unit 3 Work, Energy, and Power (15 to 25%)

Translational kinetic energy and the work-energy theorem, work as the integral of a variable force, potential energy and the relation $F = -dU/dx$, conservation of energy with and without dissipation, and power as $dW/dt$ and $\vec{F}\cdot\vec{v}$.

Unit 4 Linear Momentum (10 to 20%)

Linear momentum as a vector, impulse as the time integral of force, conservation of momentum for isolated systems, and elastic, inelastic and perfectly inelastic collisions in one and two dimensions.

Unit 5 Torque and Rotational Dynamics (10 to 15%)

Rotational kinematics, connecting linear and rotational motion, torque as a cross product, the moment of inertia by integration and the parallel-axis theorem, rotational equilibrium, and Newton's second law in rotational form.

Unit 6 Energy and Momentum of Rotating Systems (10 to 15%)

Rotational kinetic energy, the work done by a torque, angular momentum and angular impulse, conservation of angular momentum, rolling without slipping, and the motion of orbiting satellites.

Unit 7 Oscillations (10 to 15%)

Simple harmonic motion and the linear restoring force, the differential equation and its sinusoidal solution, the period of the mass-spring system and the pendulum, the energy of oscillators, and the simple and physical pendulums.

Exam structure

The AP Physics C: Mechanics exam is 3 hours and has two equally weighted sections. From 2025 it is delivered digitally in Bluebook. A calculator is allowed throughout, and you are given an equations and constants sheet.

• Section I, multiple choice - 40 questions in 80 minutes, 50%, four options each. Individual questions and question sets, many built on data, graphs, free-body diagrams or experimental setups.
• Section II, free response - 4 questions in 100 minutes, 50%. Free-response questions written from the science practices, including symbolic derivations (often using calculus), experimental design and analysis, and quantitative problem solving.

The free-response questions ask you to create and interpret representations, carry out mathematical routines including derivatives and integrals, design and analyze experiments, and construct evidence-based arguments using AP task verbs (Calculate, Derive, Describe, Explain, Justify, Determine).

How to study AP Physics C Mechanics

AP Physics C rewards fluent calculus, clear representations and confident reasoning from forces to motion.

1. Work from the Course and Exam Description. Each topic (for example 2.9 Resistive Forces) maps to specific learning objectives and essential-knowledge statements that exam questions are written from.
2. Make the calculus automatic. Differentiating position for velocity and acceleration, integrating acceleration or a variable force, and setting up the moment-of-inertia integral should be second nature; most lost marks come from calculus slips, not physics.
3. Draw the diagram first. A correct free-body diagram or motion graph starts almost every problem; on rotation problems, identify which force produces the torque.
4. Reason from the differential equation. Resistive forces and oscillations are defined by differential equations; learn to set them up, find the steady state (terminal velocity, equilibrium) and recognize the exponential or sinusoidal solution.
5. Rehearse symbolic derivations. Section II often asks you to derive a result in symbols before substituting numbers; practice deriving the standard results (orbital speed, rolling acceleration, pendulum period) cleanly.

The units, topic by topic

Each topic has a Course-and-Exam-Description-level answer page with worked exam questions and cross-links, plus an overview guide and quiz. This library covers all seven units in full:

• Unit 1: scalars and vectors, displacement, velocity and acceleration, representing motion, reference frames and relative motion, vectors and motion in two dimensions.
• Unit 2: systems and center of mass, forces and free-body diagrams, Newton's third law, Newton's first law, Newton's second law, gravitational force, kinetic and static friction, spring forces, resistive forces, circular motion.
• Unit 3: translational kinetic energy, work, potential energy, conservation of energy, power.
• Unit 4: linear momentum, change in momentum and impulse, conservation of linear momentum, collisions.
• Unit 5: rotational kinematics, connecting linear and rotational motion, torque, rotational inertia, rotational equilibrium and Newton's first law, Newton's second law in rotational form.
• Unit 6: rotational kinetic energy, torque and work, angular momentum and angular impulse, conservation of angular momentum, rolling, motion of orbiting satellites.
• Unit 7: defining simple harmonic motion, frequency and period of SHM, representing and analyzing SHM, energy of simple harmonic oscillators, simple and physical pendulums.

You can also work through the using calculus in mechanics problems skills guide and its paired quiz.

For the official Course and Exam Description

The College Board publishes the full Course and Exam Description, released free-response questions, scoring guidelines and the equations sheet at apcentral.collegeboard.org. Always study from the current Course and Exam Description and the College Board's own released exams, because question style and the science practices are board-specific.