AP Physics C: Mechanics 1-Month Study Plan

You have four weeks until the AP Physics C: Mechanics exam. This plan spreads learning across four weeks, each with a clear theme: Week 1 covers foundations (kinematics and dynamics), Week 2 tackles energy and momentum, Week 3 introduces rotation and oscillations with a mock exam, and Week 4 refines gravitation, FRQ technique, and final review.

Commit 1–1.5 hours per day, 6 days a week, with one rest day.

Week 1: Kinematics and Dynamics Foundations

Theme: Build comfort with calculus and free body diagrams.

Day	Topic	Daily Target
Mon	$v = dx/dt$ , $a = dv/dt$ , constant- $a$ equations	Read 2 worked examples; solve 10 MCQs on kinematics
Tue	Integration: $a(t) \to v(t) \to x(t)$	Solve 3 kinematics problems requiring integration; sketch 5 $x(t)$ , $v(t)$ , $a(t)$ graphs
Wed	Projectile motion (2D kinematics)	Solve 2 full projectile problems (separate $x$ and $y$ ); 12 MCQs
Thu	Free body diagrams and components	Draw FBDs for 5 scenarios (incline, tension, friction); identify $\Sigma F_x$ , $\Sigma F_y$
Fri	Newton's second law: $\Sigma F = ma$ in components	Solve 4 dynamics problems (at least one with friction); 15 MCQs
Sat	Week 1 review + problem set	Mixed 20 MCQs (kinematics + dynamics); solve 1 FRQ combining both
Sun	Rest / light review	Skim formulas; do not solve new problems

Week 1 Takeaway: You must set up and integrate $a(t)$ automatically. You must draw an FBD before writing a dynamics equation. If you can do both, you've cracked 40% of the exam.

Week 2: Energy, Momentum, and Work

Theme: Master the two great conservation laws.

Day	Topic	Daily Target
Mon	Work: $W = F \cos\theta \cdot d$ and $W = \int F \, dx$	Solve 3 work problems (constant and variable force); compute work from graphs
Tue	Kinetic energy, potential energy, conservative forces	Solve 4 energy problems; derive $F = -dU/dx$ from two examples
Wed	Energy conservation and mechanical energy	Solve 2 energy conservation problems (one with friction, one without); 14 MCQs
Thu	Linear momentum, impulse, $J = \Delta p$	Solve 3 impulse-momentum problems; compute impulse from force-time graphs
Fri	Collisions: elastic and inelastic, momentum conservation	Solve 2 collision problems (elastic and inelastic); 15 MCQs on momentum
Sat	Week 2 review + FRQs	Mixed 20 MCQs (energy + momentum); solve 2 FRQs (one energy, one collision)
Sun	Rest / light review	Skim conservation laws; review one worked example per law

Week 2 Takeaway: Every energy or momentum problem starts with "Is mechanical energy conserved? Is momentum conserved?" If yes, set up $E_i = E_f$ or $p_i = p_f$ . If no, explain why (non-conservative forces, external impulse).

Week 3: Rotation, Oscillations, and Mock Exam #1

Theme: Master rotational dynamics and SHM; take a full practice exam.

Day	Topic	Daily Target
Mon	Moment of inertia: definition and standard values	Derive or memorize $I$ for 4 shapes (rod, disk, sphere, hoop); solve 2 problems
Tue	Parallel-axis theorem; applying $\tau = I\alpha$	Solve 3 torque problems; compute $I$ about different axes
Wed	Angular momentum $L = I\omega$ , conservation	Solve 2 angular momentum conservation problems; 12 MCQs on rotation
Thu	Simple harmonic motion: $\ddot{x} + \omega^2 x = 0$ , period $T = 2\pi\sqrt{m/k}$	Solve 3 SHM problems (springs, pendulums); energy in SHM
Fri	Rolling without slipping; rotational + translational KE	Solve 2 rolling problems (find speed using energy conservation)
Sat	Mock Exam #1 (full-length, timed)	35 MCQs (45 min) + 3 FRQs (45 min). Score and review.
Sun	Review mock, rest	Analyze weak spots; review one FRQ solution

Week 3 Takeaway: Rotation is not separate physics — it's the same $F = ma$ rotated. Think $\Sigma \tau = I\alpha$ as the rotational version of $\Sigma F = ma$ . Parallel-axis theorem is tricky; practice one derivation carefully.

Week 4: Gravitation, FRQ Mastery, and Final Review

Theme: Finish gravitation, refine FRQ technique, take a second mock, then rest.

Day	Topic	Daily Target
Mon	Newton's law of gravitation $F = GMm/r^2$ , potential energy $U = -GMm/r$	Solve 3 gravitation problems; understand why $U$ is negative
Tue	Escape velocity $v_{esc} = \sqrt{2GM/R}$ , orbital speed $v = \sqrt{GM/r}$	Solve 2 orbital problems; derive orbit speed from centripetal acceleration
Wed	Kepler's third law $T^2 \propto a^3$ , satellite motion	Solve 3 problems on satellites and orbits; 14 MCQs on gravitation
Thu	FRQ technique: setting up integrals, citing conservation, drawing FBDs	Solve 2–3 FRQ-style problems; focus on clear notation and complete steps
Fri	Mock Exam #2 (full-length, timed)	35 MCQs (45 min) + 3 FRQs (45 min). Compare with Mock #1.
Sat	Review Mock #2, identify weak points	Rework one FRQ from each weak unit; do not learn new material
Sun	Rest and review last-minute checklist	Sleep 8+ hours. Do not cram.

Week 4 Takeaway: By now, your strength on FRQs is writing the integral or differentiation first, then evaluating. Your weakness is likely forgetting to state conservation conditions or missing a sign. Fix these before the exam.

Weekly Review Checklist

After each week (especially after mocks), ask yourself:

Can I derive or recall all standard moments of inertia ( $I = \frac{1}{12}ML^2$ , $I = \frac{1}{2}MR^2$ , etc.)?
Can I set up and solve an integral for work, impulse, or moment of inertia from first principles?
Can I draw an FBD and resolve forces into components without hesitation?
Can I apply conservation of energy and momentum and explain why they apply?
Do I know Kepler's third law and escape velocity well enough to explain them in 30 seconds?

If the answer to any is "no," spend 1 hour on that topic during the next week's rest day.

Practice Resource Strategy

Weeks 1–2: Mostly MCQs and single-topic problems (low FRQ ratio).
Week 3: Mix MCQs with more FRQ-style problems; take a full mock.
Week 4: FRQ-heavy review; take a second mock; focus on weak points.

Score targets by week (rough guidance)

After Week 1: You should pass a quiz on kinematics + dynamics (~50–60% on a timed set).
After Week 2: You should pass a quiz on energy + momentum (~50–60%).
After Week 3 mock: You should score ~50–55% raw (equivalent to a 4–5 on the actual exam).
After Week 4: You should score ~55–60% raw on the final mock (equivalent to a solid 5).

Remember: Physics C is curved generously. A raw score of 50% is often a 5. Do not panic if you're not at 80%.

Ready to start Week 1? Jump to Kinematics → and begin Monday.