AP Physics C: Mechanics 3-Day Cram Plan

You have three days until the AP Physics C: Mechanics exam. This is not the time to learn vector calculus or derive the parallel-axis theorem from scratch — it's time to drill the highest-frequency topics and lock in the patterns that appear on every exam.

This plan assumes ~4 focused hours per day. The exam is 90 minutes (35 MCQ + 3 FRQ), and you only need ~50% to score a 5. But 50% at 90 minutes is fast — practice speed.

Day 1: Kinematics and Dynamics with Calculus (4 hrs)

The first 15–20 MCQs test your comfort with the fundamental calculus relationships: $v = dx/dt$, $a = dv/dt$, and integrating acceleration to find velocity and position.

What to review (90 min)

• Position, velocity, acceleration: know $v(t) = \frac{dx}{dt}$ and $a(t) = \frac{dv}{dt}$ cold. If given $a(t)$, integrate to get $v(t)$, then integrate again for $x(t)$.
• Constant acceleration kinematics: $v = v_0 + at$, $x = v_0 t + \frac{1}{2}at^2$, $v^2 = v_0^2 + 2a(x - x_0)$. Use these shortcuts when $a$ is constant.
• Projectile motion: horizontal component (no acceleration) vs. vertical (free fall). Set up $x(t)$ and $y(t)$ separately.
• Free body diagrams (FBDs): draw every force, label directions, resolve into components ($x$, $y$). This is non-negotiable on FRQs.
• Newton's second law in components: $\Sigma F_x = ma_x$, $\Sigma F_y = ma_y$. Friction $f = \mu N$, normal force from constraint.

What to practice (2.5 hrs)

• 20 MCQs on kinematics: given $a(t)$, find $v(t)$ via integration; given position vs. time, identify acceleration from the graph.
• 1 full FRQ on projectile motion with calculus (e.g., "A ball is thrown; given $v_y(t) = 20 - 10t$, find position, maximum height, time to hit the ground").

💡 Highest leverage: Every single 3-FRQ exam includes at least one kinematics or dynamics problem. If you can set up and integrate $a(t)$ to find $v$ and $x$, you've earned 40% of FRQ points.

Common mistakes tonight

• Forgetting that $v$ and $a$ are vectors — direction matters. A negative acceleration doesn't mean slowing down if velocity is also negative.
• Confusing $v_0$ (initial velocity) with velocity at $t = 0$. Always define your coordinate system first.
• Skipping the FBD. On every FRQ, draw the diagram before you write an equation.

Day 2: Energy, Momentum, and Work (4 hrs)

Together, conservation of energy and momentum account for ~30–35% of the exam. These are the "big two" conservation laws.

What to review (90 min)

• Work by a constant force: $W = F \cos\theta \cdot d = \vec F \cdot \vec d$.
• Work by a variable force: $W = \int \vec F \cdot d\vec r$. If force depends on position, integrate.
• Kinetic energy: $KE = \frac{1}{2}mv^2$. Relate to work via work-energy theorem: $W_{net} = \Delta KE$.
• Potential energy: gravitational $U_g = mgh$ (near Earth surface), elastic $U_s = \frac{1}{2}kx^2$, and derive $F = -\frac{dU}{dx}$ (force is negative gradient of potential).
• Conservation of mechanical energy: $E = KE + U = \text{constant}$ if only conservative forces do work. Set up $E_i = E_f$.
• Impulse and momentum: $J = \int F \, dt = \Delta p = m\Delta v$. On a graph, impulse is area under the force-time curve.
• Conservation of linear momentum: $p_i = p_f$ if net external force is zero (e.g., collisions in isolation).

What to practice (2.5 hrs)

• 1 FRQ on energy conservation (e.g., block sliding down an incline with friction; find final speed).
• 1 FRQ on momentum conservation (e.g., collision with a spring, or explosion).
• 18 MCQs on energy and momentum, mixing graphs and calculations.

⚠️ FRQ trap: When you cite "conservation of mechanical energy," you must state the conditions: no non-conservative forces (like friction) do work, or if they do, account for them explicitly: $E_i + W_{friction} = E_f$. Examiners are strict about this.

Day 3: Rotation, Oscillations, Gravitation + Mock FRQ (4 hrs)

These three topics fill the remaining time on exam day. Rotation is the heaviest hitter.

What to review (90 min)

• Moment of inertia: $I = \int r^2 \, dm$. Know standard values: rod through center $I = \frac{1}{12}ML^2$, disk/cylinder $I = \frac{1}{2}MR^2$, sphere $I = \frac{2}{5}MR^2$, hoop $I = MR^2$. Parallel-axis theorem: $I = I_{cm} + Md^2$.
• Torque and angular acceleration: $\tau = I\alpha$, just like $F = ma$ for rotation. Sum torques about a fixed axis.
• Angular momentum: $L = I\omega$ for a rigid body; $L = \vec r \times \vec p$ for a point particle. Conservation: if net torque is zero, $L$ is constant.
• Rotational kinetic energy: $KE_{rot} = \frac{1}{2}I\omega^2$. Use in energy conservation alongside translational $KE = \frac{1}{2}mv^2$.
• Rolling without slipping: $v_{cm} = R\omega$ and $a_{cm} = R\alpha$. Total kinetic energy: $KE = \frac{1}{2}mv_{cm}^2 + \frac{1}{2}I\omega^2$.
• Simple harmonic motion (SHM): differential equation $\ddot{x} + \omega^2 x = 0$; solution $x(t) = A\cos(\omega t + \phi)$. Period: $T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{m}{k}}$ for a spring. Energy in SHM: $E = \frac{1}{2}kA^2 =$ constant.
• Gravitation: Newton's law $F = \frac{Gm_1 m_2}{r^2}$. Gravitational potential energy: $U_g = -\frac{GMm}{r}$. Escape velocity: $v_{esc} = \sqrt{\frac{2GM}{R}}$. Orbital speed: $v_{orbit} = \sqrt{\frac{GM}{r}}$ (from $a = \frac{v^2}{r}$). Kepler's third law: $T^2 \propto a^3$.

What to practice (2.5 hrs — timed full-length set)

• 1 full FRQ on rotation (e.g., moment of inertia from integration, or angular momentum conservation in a collision).
• 1 full FRQ mixing two topics (e.g., energy in a rolling cylinder going down an incline, or SHM with energy).
• 25 MCQs across all three units, strictly timed.

🎯 Key insight: Rotation often appears with integration (computing $I$ from $\int r^2 \, dm$). Oscillation often pairs with energy (finding amplitude from energy conservation). Gravitation tests Kepler's laws and escape velocity. Know one worked example per topic cold.

The night before

Skim the last-minute review checklist. Get 8 hours of sleep. On exam day, you'll be asked to cite conservation laws by name, draw clear FBDs, and show all integral steps — a rested brain does all three.

What this 3-day plan deliberately skips

You will not fully re-derive the parallel-axis theorem or solve all SHM initial-condition problems. If you're shaky: skim one derivation, do 2–3 worked examples, move on. Spend your time on the FRQ patterns that must appear: kinematics via calculus, energy/momentum conservation, and one rotation or gravitation problem.

Ready to start?

Open the AP Physics C: Mechanics topic library → and tackle Day 1 kinematics problems now. You've got this. 🎯