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AP Physics C Mechanics · Reference

AP Physics C Mechanics formula sheet every equation by topic.

Here is the full AP Physics C Mechanics formula sheet, also called the equation sheet, organized by topic from kinematics to gravitation. The College Board provides this calculus-based reference for both sections on exam day — so the goal is to know which equation and which calculus step a problem needs, not to memorize the list.

Updated June 2026Part of AP Physics C Mechanics Review

Is the equation sheet provided on the AP Physics C Mechanics exam?

Yes. The official AP Physics C Mechanics equation sheet is provided for both the multiple-choice and free-response sections, and a calculator is allowed throughout. Because this is the calculus-based course, the sheet gives you the formulas but assumes you can already take derivatives and evaluate integrals — it does not include integration techniques.

The version below is grouped the way the course is taught, so each equation connects to the unit it belongs to.

The AP Physics C Mechanics equation sheet, by topic

Every relationship you are handed on test day, with a plain-language note on when to use it.

Kinematics

v = dx/dt,  a = dv/dt
Velocity and acceleration as derivatives — the calculus form.
v = v0 + at
Velocity under constant acceleration.
x = x0 + v0t + ½at2
Position under constant acceleration.
v2 = v02 + 2a(x − x0)
Velocity from displacement.

Forces & dynamics

ΣF = ma = dp/dt
Newton’s second law, including its momentum form.
Ff ≤ μN
Friction force.
Fs = −kx
Hooke’s law for a spring.
ac = v2/r
Centripetal acceleration.

Work, energy & power

W = ∫F·dx
Work as the integral of force over distance.
K = ½mv2
Kinetic energy.
Us = ½kx2
Spring potential energy.
P = dW/dt = F·v
Power.

Linear momentum

p = mv
Linear momentum.
J = ∫F dt = Δp
Impulse equals the change in momentum.
xcm = (Σmixi) / Σmi
Center of mass.

Rotation

τ = rF·sinθ = Iα
Torque, and its rotational Newton’s-second-law form.
I = ∫r2 dm
Moment of inertia.
L = Iω
Angular momentum.
Krot = ½Iω2
Rotational kinetic energy.
ω = ω0 + αt
Rotational kinematics.

Oscillations

Ts = 2π√(m/k)
Period of a mass on a spring.
Tp = 2π√(L/g)
Period of a simple pendulum.
x(t) = A·cos(ωt + φ)
Position in simple harmonic motion.

Gravitation & orbits

Fg = Gm1m2/r2
Newton’s law of universal gravitation.
Ug = −Gm1m2/r
Gravitational potential energy.
T2 ∝ r3
Kepler’s third law for orbits.

Constants provided on the sheet

G = 6.67 × 10−11 N·m2/kg2
Universal gravitational constant.
g = 9.8 m/s2
Acceleration due to gravity near Earth’s surface.

How the Physics C and Physics 1 sheets differ

They cover similar mechanics topics, but the Physics C Mechanics sheet is written in calculus — you will see derivative and integral forms like a = dv/dt and W = ∫F·dx that the algebra-based Physics 1 sheet does not use. The trade-off is that Physics C expects you to actually perform those calculus steps.

How to use the equation sheet

Treat the sheet as a map, not a crutch. In your studying, practice naming which equation and which calculus operation a problem calls for, because that judgment is exactly what the exam tests. Knowing the layout also saves time under pressure.

When you want to use these equations in a written solution, our FRQ guide shows how the free response is scored, and the score calculator turns a practice raw score into a 1–5.

Frequently asked questions

Quick answers — written by humans, not a chatbot.

Is the AP Physics C Mechanics equation sheet provided on the exam?

Yes — it is available for both sections, along with a calculator, so you do not memorize the formulas.

Is the AP Physics C Mechanics equation sheet calculus-based?

Yes. It includes calculus forms like a = dv/dt and W = ∫F·dx, but it does not include integration techniques — you are expected to know calculus.

What is the difference between the Physics C and Physics 1 equation sheets?

They share mechanics topics, but the Physics C sheet uses calculus (derivative and integral forms) while the Physics 1 sheet is algebra-based.

Do I need to memorize formulas for AP Physics C Mechanics?

No — they are provided. You do need to know which equation applies and how to set up the right derivative or integral.

Can I use the equation sheet on the free-response section?

Yes. The same equation sheet is available for both the multiple-choice and free-response sections.

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