AP Physics C: Mechanics

The Physics C: Mechanics equation sheet, annotated for 2026

Transcribed from the equations table of the official AP Physics C: Mechanics Course and Exam Description (Effective Fall 2024). College Board provides this sheet on both sections of the exam, so nothing here needs memorizing; knowing when each equation applies is the skill the exam actually tests. The geometry and math reference tables printed alongside the equations are not reproduced here.

For the units these equations belong to, see the Physics C: Mechanics course hub.

Constants and Conversion Factors

G=6.67×10−11 m3/(kg⋅s2)=6.67×10−11 N⋅m2/kg2G = 6.67 \times 10^{-11}\ \text{m}^3/(\text{kg} \cdot \text{s}^2) = 6.67 \times 10^{-11}\ \text{N} \cdot \text{m}^2/\text{kg}^2

Universal gravitational constant

g=9.8 m/s2g = 9.8\ \text{m/s}^2

Magnitude of the acceleration due to gravity at Earth's surface

g=9.8 N/kgg = 9.8\ \text{N/kg}

Magnitude of the gravitational field strength at Earth's surface

Mechanics

vx=vx0+axtv_x = v_{x0} + a_x t
x=x0+vx0t+12axt2x = x_0 + v_{x0} t + \frac{1}{2} a_x t^2
vx2=vx02+2ax(x−x0)v_x^2 = v_{x0}^2 + 2 a_x (x - x_0)
Δx=∫vx(t) dt\Delta x = \int v_x(t)\, dt
Δvx=∫ax(t) dt\Delta v_x = \int a_x(t)\, dt
x⃗cm=∑mix⃗i∑mi\vec{x}_{\text{cm}} = \frac{\sum m_i \vec{x}_i}{\sum m_i}
r⃗cm=∫r⃗ dm∫dm\vec{r}_{\text{cm}} = \frac{\int \vec{r}\, dm}{\int dm}
λ=ddℓm(ℓ)\lambda = \frac{d}{d\ell} m(\ell)
a⃗sys=∑F⃗msys=F⃗netmsys\vec{a}_{\text{sys}} = \frac{\sum \vec{F}}{m_{\text{sys}}} = \frac{\vec{F}_{\text{net}}}{m_{\text{sys}}}
∣F⃗g∣=Gm1m2r2\left| \vec{F}_g \right| = \frac{G m_1 m_2}{r^2}
∣F⃗f∣≤∣μF⃗N∣\left| \vec{F}_f \right| \leq \left| \mu \vec{F}_N \right|
F⃗s=−kΔx⃗\vec{F}_s = -k \Delta \vec{x}
ac=v2r=rω2a_c = \frac{v^2}{r} = r \omega^2
T=1fT = \frac{1}{f}
K=12mv2K = \frac{1}{2} m v^2
W=∫abF⃗⋅dr⃗W = \int_a^b \vec{F} \cdot d\vec{r}
ΔK=∑Wi=∑F∥,i di\Delta K = \sum W_i = \sum F_{\parallel, i}\, d_i
ΔU=−∫abF⃗cf(r)⋅dr⃗\Delta U = -\int_a^b \vec{F}_{\text{cf}}(r) \cdot d\vec{r}
Fx=−dU(x)dxF_x = -\frac{dU(x)}{dx}
Us=12k(Δx)2U_s = \frac{1}{2} k (\Delta x)^2
UG=−Gm1m2rU_G = -\frac{G m_1 m_2}{r}
ΔUg=mgΔy\Delta U_g = m g \Delta y
Pavg=WΔt=ΔEΔtP_{\text{avg}} = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t}
Pinst=dWdtP_{\text{inst}} = \frac{dW}{dt}
p⃗=mv⃗\vec{p} = m \vec{v}
F⃗net=dp⃗dt\vec{F}_{\text{net}} = \frac{d\vec{p}}{dt}
J⃗=∫t1t2F⃗net(t) dt=Δp⃗\vec{J} = \int_{t_1}^{t_2} \vec{F}_{\text{net}}(t)\, dt = \Delta \vec{p}
v⃗cm=∑p⃗i∑mi=∑miv⃗i∑mi\vec{v}_{\text{cm}} = \frac{\sum \vec{p}_i}{\sum m_i} = \frac{\sum m_i \vec{v}_i}{\sum m_i}
ω=dθdt\omega = \frac{d\theta}{dt}
α=dωdt\alpha = \frac{d\omega}{dt}
ω=ω0+αt\omega = \omega_0 + \alpha t
θ=θ0+ω0t+12αt2\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2
ω2=ω02+2α(θ−θ0)\omega^2 = \omega_0^2 + 2 \alpha (\theta - \theta_0)
v=rωv = r \omega
aT=rαa_T = r \alpha
τ⃗=r⃗×F⃗\vec{\tau} = \vec{r} \times \vec{F}
Itot=∑Ii=∑miri2I_{\text{tot}} = \sum I_i = \sum m_i r_i^2
I=∫r2 dmI = \int r^2\, dm
I′=Icm+Md2I' = I_{\text{cm}} + M d^2
αsys=∑τIsys=τnetIsys\alpha_{\text{sys}} = \frac{\sum \tau}{I_{\text{sys}}} = \frac{\tau_{\text{net}}}{I_{\text{sys}}}
Krot=12Iω2K_{\text{rot}} = \frac{1}{2} I \omega^2
W=∫τ⋅dθW = \int \tau \cdot d\theta
L⃗=r⃗×p⃗=Iω⃗\vec{L} = \vec{r} \times \vec{p} = I \vec{\omega}
ΔL=∫τ dt\Delta L = \int \tau\, dt
Δxcm=rΔθ\Delta x_{\text{cm}} = r \Delta\theta
T=2πω=1fT = \frac{2\pi}{\omega} = \frac{1}{f}
Ts=2πmkT_s = 2\pi \sqrt{\frac{m}{k}}
Tp=2πℓgT_p = 2\pi \sqrt{\frac{\ell}{g}}
Tphys=2πImgdT_{\text{phys}} = 2\pi \sqrt{\frac{I}{m g d}}
x=xmaxcos⁡(ωt+ϕ)x = x_{\text{max}} \cos(\omega t + \phi)

The other sheets

AP Physics 1: Algebra-Based52 constants and equations, grouped as printed.AP Physics 2: Algebra-Based129 constants and equations, grouped as printed.AP Physics C: Electricity and Magnetism103 constants and equations, grouped as printed.Physics C: Mechanics: the course, unit by unitUnits, weightings, topics, exam format, and the May 2025 score results.