AP Physics C: Mechanics Last-Minute Review (Night Before)

The exam is tomorrow. This is not the time to learn the parallel-axis theorem — it's time to skim, organize, sleep, and calm your nerves. Spend 45 minutes on this page, then put notes away.

Core Kinematic and Dynamics Equations

Quantity	Formula	Notes
Velocity from acceleration	$v = v_0 + \int a \, dt$	Integrate; if $a$ is constant, $v = v_0 + at$
Position from velocity	$x = x_0 + \int v \, dt$	Integrate; if $v$ is constant, $x = x_0 + vt$
Newton's second law	$\Sigma F = ma$	Always resolve into components ( $x$ , $y$ )
Friction (kinetic)	$f_k = \mu_k N$	Opposes motion; maximum static is $f_s \leq \mu_s N$
Weight	$W = mg$	Near Earth, $g \approx 10 \, \text{m/s}^2$

Work, Energy, and Power

Quantity	Formula	Notes
Work by constant force	$W = F\cos\theta \cdot d$	Can also be $W = \vec F \cdot \vec d$
Work by variable force	$W = \int \vec F \cdot d\vec r$	Integrate along the path
Kinetic energy	$KE = \frac{1}{2}mv^2$	Always positive
Gravitational PE (near Earth)	$U_g = mgh$	Relative; choose $h = 0$ arbitrarily
Elastic PE (spring)	$U_s = \frac{1}{2}kx^2$	$x$ is stretch from equilibrium
Force from PE	$F = -\frac{dU}{dx}$	Differentiate potential to find force
Power	$P = \frac{dE}{dt} = \vec F \cdot \vec v$	Rate of energy transfer

Momentum and Impulse

Quantity	Formula	Notes
Linear momentum	$p = mv$	Vector; units: kg·m/s
Impulse	$J = \int F \, dt = \Delta p$	Area under force-time curve
Collision (elastic)	$v_1' = \frac{(m_1 - m_2)v_1 + 2m_2 v_2}{m_1 + m_2}$	Both $KE$ and $p$ conserved
Collision (perfectly inelastic)	$v' = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$	Objects stick; only $p$ conserved

Rotation

Quantity	Formula	Notes
Angular velocity	$\omega = \frac{d\theta}{dt}$	Radians per second
Angular acceleration	$\alpha = \frac{d\omega}{dt}$	Radians per second squared
Moment of inertia (definition)	$I = \int r^2 \, dm$	Compute via integration or use standard values below
Torque	$\tau = r F \sin\theta = I\alpha$	Angular version of $F = ma$
Angular momentum	$L = I\omega$	Conserved if net torque is zero
Rotational kinetic energy	$KE_{rot} = \frac{1}{2}I\omega^2$	Add to translational $KE$ for rolling
Rolling without slipping	$v = R\omega$ and $a = R\alpha$	Constraint between linear and angular motion

Moments of Inertia (Standard Shapes)

Shape	Axis	Moment of Inertia
Thin rod of length $L$ , mass $M$	Through center, perpendicular to rod	$I = \frac{1}{12}ML^2$
Thin rod of length $L$ , mass $M$	Through one end, perpendicular to rod	$I = \frac{1}{3}ML^2$
Disk or cylinder, mass $M$ , radius $R$	Through center, along axis	$I = \frac{1}{2}MR^2$
Solid sphere, mass $M$ , radius $R$	Through center	$I = \frac{2}{5}MR^2$
Thin spherical shell, mass $M$ , radius $R$	Through center	$I = \frac{2}{3}MR^2$
Hoop or hollow cylinder, mass $M$ , radius $R$	Through center, along axis	$I = MR^2$
Parallel-axis theorem	Object at distance $d$ from center	$I = I_{cm} + Md^2$

Parallel-axis trap: $d$ is the distance from the center of mass to the new axis, not from the original axis. Draw a diagram.

Simple Harmonic Motion

Quantity	Formula	Notes
SHM differential equation	$\ddot{x} + \omega^2 x = 0$	General solution: $x(t) = A\cos(\omega t + \phi)$
Angular frequency	$\omega = \sqrt{\frac{k}{m}}$ (spring), $\omega = \sqrt{\frac{g}{L}}$ (pendulum)	Radians per second
Period	$T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{m}{k}}$ (spring), $T = 2\pi\sqrt{\frac{L}{g}}$ (small-angle pendulum)	Seconds
Total energy in SHM	$E = \frac{1}{2}kA^2 = \text{const}$	At maximum displacement, all PE; at equilibrium, all KE

Gravitation

Quantity	Formula	Notes
Newton's law of gravitation	$F = \frac{Gm_1 m_2}{r^2}$	$G = 6.67 \times 10^{-11} \, \text{N·m}^2/\text{kg}^2$
Gravitational PE	$U_g = -\frac{GMm}{r}$	Negative; zero at infinity; more negative closer to Earth
Gravitational field	$g = \frac{GM}{r^2}$	Acceleration due to gravity at radius $r$
Escape velocity	$v_{esc} = \sqrt{\frac{2GM}{R}}$	Minimum speed to escape to infinity
Orbital speed	$v_{orbit} = \sqrt{\frac{GM}{r}}$	Gravitational force provides centripetal acceleration
Orbital period	$T = 2\pi\sqrt{\frac{r^3}{GM}}$	From Kepler's third law: $T^2 \propto r^3$ (or $T^2 \propto a^3$ )

The Three Great Conservation Laws

1. Conservation of Mechanical Energy

$E = KE + U = \text{constant}$

Conditions: Only conservative forces (gravity, springs) do work, or non-conservative work is accounted for: $E_i + W_{\text{non-conservative}} = E_f$

On the exam: Always state these conditions. Examiners are strict.

2. Conservation of Linear Momentum

$p_i = p_f \quad \text{(or } \Sigma p_x = \text{const}, \Sigma p_y = \text{const} \text{)}$

Conditions: No net external force acts on the system. Collisions between two objects satisfy this automatically (internal forces cancel).

Trap: If there's friction with the ground or an external applied force, momentum is not conserved for a single object. It IS conserved for two objects colliding if we ignore air resistance.

3. Conservation of Angular Momentum

$L_i = L_f \quad \text{(or } L = I\omega = \text{constant)}$

Conditions: No net external torque acts on the system about the chosen axis.

Top 10 Point-Losing Traps

Forgetting units. "5 m/s" not just "5". "12 joules", not "12".
Confusing $v$ and $|v|$ (speed). In SHM, $v$ changes sign; speed doesn't.
Forgetting the negative sign on gravitational PE. $U = -GMm/r$ (negative!).
Parallel-axis theorem misapplied. $I = I_{cm} + Md^2$ , where $d$ is distance from the center of mass to the new axis.
Not citing conservation law conditions. "Mechanical energy is conserved" is incomplete. Say: "Mechanical energy is conserved because only gravity acts; air resistance is negligible."
Energy conservation with friction. Don't forget $W_{friction} = E_i - E_f$ . Friction removes energy.
Angular momentum: wrong axis. $L = I\omega$ only if $I$ is about the axis you're summing torques around. If the axis changes, angular momentum is not conserved.
Moment of inertia for the wrong shape. Know your $I$ table cold. A disk is $\frac{1}{2}MR^2$ , a sphere is $\frac{2}{5}MR^2$ .
Collision: forgetting that kinetic energy is not conserved (unless the problem says "elastic"). In inelastic collisions, $KE_i > KE_f$ .
Escape velocity vs. orbital speed. Escape is $\sqrt{2GM/R}$ ; orbit is $\sqrt{GM/r}$ . Escape is $\sqrt{2}$ times faster than an orbit at the surface.

Exam Strategy

Multiple Choice (45 min for 35 questions)

Mark and skip anything that takes > 90 seconds. Rough order: 1.3 min per question on average.
Read the question twice. Misreading is the #1 error. "How much time" vs. "at what time"?
Eliminate obviously wrong answers first. If the answer has the wrong units or absurd magnitude, cross it out.
If stuck, guess — there's no penalty for a blank. (Actually there is: zero points. A 25% guess is better.)

Free Response (45 min for 3 FRQs)

Read all three FRQs first. Start with the one you're most confident on.
Draw a free body diagram before you write a force equation. Even if it's quick, do it.
Show the integral or derivative. Write $v = \int a \, dt$ before plugging in numbers. Graders give partial credit for the setup.
State your conservation law. Don't just say "energy is conserved." Say: "Mechanical energy is conserved because only gravity acts."
Don't leave anything blank. A half-finished FRQ earns partial credit. A blank earns zero.

Timing

Spend 45 min on MCQ, leaving 0 min buffer (move steadily; don't panic).
Spend 15 min per FRQ. If you're over, switch to the next one and come back if time remains.

Score Boundaries (Recent Years)

Approximate out of ~75 raw points:

Score	Raw Points (approx)	Percentage
5	50–75	67–100%
4	40–49	53–66%
3	30–39	40–52%
2	20–29	27–39%
1	below 20	below 27%

Physics C is curved generously. You can score a 5 with just 50% correct. You do not need to be perfect.

Morning-of Checklist

☐ 8+ hours of sleep. Non-negotiable. A tired brain misreads $F = ma$ as $F = m/a$ .
☐ Real breakfast: protein + complex carbs. Eggs and oatmeal, not just sugar.
☐ 2 sharpened #2 pencils, eraser, black or blue pen for FRQs.
☐ Approved calculator (graphing OK; CAS typically not OK — check your school). Spare batteries.
☐ Photo ID + AP ID label (if provided).
☐ Water, snack for the break. Banana, nuts, etc.
☐ Arrive 30 min early. Rushing introduces careless errors.

During the Exam

Breathe. Seriously. When you feel stuck, take 3 deep breaths. Panic kills problem-solving.
Check your algebra. Before you finalize an answer, plug numbers back in to verify.
Don't second-guess yourself. If you're confident in an answer, move on. Overthinking costs time.
Mark tough questions. On MCQ, mark with a checkmark and come back if there's time after you finish.
Write neatly on FRQs. Graders can only score what they can read. Illegible = no points.

One Last Thing

You've prepared. The work is done. Trust yourself. Show up rested, read each question carefully, cite your conservation laws, and don't panic if something looks unfamiliar — the exam is designed to include some novel setups. Your job is to recognize the underlying physics (Newton's second law, energy, momentum, angular momentum) and apply it.

Good luck. You've got this. 🎯

Need more focused review? Revisit the 3-day cram plan →, FRQ practice guide →, or topic library →.