AP Physics C: Mechanics Study Guide

The course is a calculus-based tour of classical mechanics. You start with kinematics, now defining velocity and acceleration as derivatives and recovering position by integration, then build Newton's laws of motion into problems with variable forces, including drag where $F$ depends on velocity and you must solve a differential equation.

From there the conservation tools arrive: work, energy, and power (with work as the integral $\int Fdx$) and linear momentum (with impulse as $\int Fdt$). The back half generalizes everything to rotation — torque, rotational inertia from $\int r^{2}dm$, and angular momentum — adds oscillations through the differential equation of simple harmonic motion, and closes with gravitation and orbital energy. The recurring theme is that calculus turns each "average" formula from the algebra course into an exact one.

The College Board does not publish fixed percentage weights for the Physics C units, so treat them as roughly comparable and let the structure guide your priorities. The seven units are:

• Kinematics — motion as derivatives and integrals
• Newton's Laws of Motion — including variable and resistive forces
• Work, Energy, and Power — work as an integral, potential-energy functions
• Linear Momentum — impulse, collisions, center of mass
• Rotation — torque, rotational inertia, angular momentum
• Oscillations — simple harmonic motion as a differential equation
• Gravitation — orbits, gravitational potential energy, Kepler's laws

The practical takeaway: forces, energy, and momentum form the core that everything else extends, and rotation re-tells those same conservation ideas with new symbols. Lock down the first four units and the rest become variations on a theme.

Physics C rewards calculus fluency layered on solid mechanics intuition. A routine that works:

1. Set up the integral or derivative explicitly. Write $a=dv/dt$ or $W=\int Fdx$ before you compute. Most lost points come from a wrong setup, not wrong arithmetic.
2. Draw first, solve second. A free-body diagram or a before/after sketch still decides the signs and the geometry; calculus only handles the bookkeeping afterward.
3. Practice variable-force problems. Drag, springs, and non-uniform mass distributions are where Physics C separates from the algebra course — and where the harder free-response points live.
4. Work in mixed sets and review with full solutions. Mixed practice forces you to choose the right tool, and reading a complete worked solution for a problem you missed teaches more than three easy ones you already knew.

• Using constant-acceleration kinematics when acceleration isn't constant — once a force depends on position or velocity, you must integrate, not plug into $v=v_0+at$.
• Botching limits of integration, or forgetting that the variable of integration must match the differential ($dx$, $dt$, or $dm$).
• Reaching for kinematics when energy or momentum is faster — if time never appears, a conservation law is usually the shortcut.
• Treating rotation as brand new instead of mapping force→torque and mass→rotational inertia, and forgetting the parallel-axis theorem.
• Vague free-response justifications. A correct number with no supporting reasoning leaves easy points on the table.

Every unit below has a focused practice set with full written explanations and a rationale for every wrong choice, plus a worked-solutions page you can read straight through. Start with a unit you're shaky on, then take a mixed set across the whole subject to pressure-test your tool selection before exam day. It's free and needs no account.