Every AP Physics 1 equation, grouped by course unit, with what each symbol stands for. Constants: g = 9.8 m/s², G = 6.67 × 10⁻¹¹ N·m²/kg².
Kinematics
v = v₀ + at
velocity after time t at constant acceleration a
x = x₀ + v₀t + ½at²
position after time t
v² = v₀² + 2a(x − x₀)
velocity after a displacement, no time needed
Force and translational dynamics
a = ΣF / m
Newton’s second law: net force over mass
|F_f| ≤ μ|F_N|
friction force is at most the coefficient of friction × normal force
F_s = −kΔx
Hooke’s law: spring force against the stretch
F_g = Gm₁m₂ / r²
gravitational force between two masses
a_c = v² / r
centripetal acceleration in a circle of radius r
Work, energy and power
K = ½mv²
kinetic energy
W = F∥d = Fd cos θ
work done by a force along the displacement
ΔU_g = mgΔy
change in gravitational potential energy near Earth
U_s = ½kx²
elastic potential energy in a spring
U_G = −Gm₁m₂ / r
gravitational potential energy of two masses
P = ΔE / Δt = Fv cos θ
power: energy per second
Linear momentum
p = mv
momentum
J = FΔt = Δp
impulse equals change in momentum
x_cm = Σmᵢxᵢ / Σmᵢ
position of the centre of mass
Torque and rotational dynamics
ω = ω₀ + αt
angular velocity at constant angular acceleration
θ = θ₀ + ω₀t + ½αt²
angle turned
ω² = ω₀² + 2α(θ − θ₀)
angular velocity after turning an angle
v = rω, a_T = rα
linking rotation to motion at radius r
τ = rF sin θ
torque
α = Στ / I
Newton’s second law for rotation
I = Σmr², I′ = I_cm + Md²
rotational inertia; parallel axis theorem
Energy and momentum of rotating systems
K = ½Iω²
rotational kinetic energy
W = τΔθ
work done by a torque
L = Iω = rmv sin θ
angular momentum
ΔL = τΔt
angular impulse
Oscillations
T = 1 / f
period and frequency
T_s = 2π√(m / k)
period of a mass on a spring
T_p = 2π√(ℓ / g)
period of a simple pendulum (small angles)
x = A cos(2πft)
position in simple harmonic motion
Fluids
ρ = m / V
density
P = F / A
pressure
P = P₀ + ρgh
pressure at depth h
F_b = ρVg
buoyant force (Archimedes)
A₁v₁ = A₂v₂
continuity: flow rate stays the same
P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂²
Bernoulli’s equation
How to use the equation sheet on the exam
List what the question gives you and what it asks for, with units.
Find the unit (kinematics, energy, momentum…) and pick the equation that links exactly those quantities.
Rearrange it with symbols first, then put the numbers in.
Check the units and whether the size of the answer makes sense.
Worked example
A ball is dropped from 20 m. How fast is it going when it hits the ground? Known: v₀ = 0, a = 9.8 m/s², x − x₀ = 20 m; no time given, so use v² = v₀² + 2a(x − x₀) = 0 + 2 × 9.8 × 20 = 392, giving v = √392 ≈ 19.8 m/s. Energy agrees: mgΔy = ½mv² gives the same v = √(2gΔy).
Do you get an equation sheet on the AP Physics 1 exam?
Yes. The College Board gives a formula sheet with the equations and constants for every unit, and you can use it in both sections. Check the official sheet for your exam year, as the course was updated for 2024–25 (fluids were added).
What units are on the AP Physics 1 exam?
Kinematics; force and translational dynamics; work, energy and power; linear momentum; torque and rotational dynamics; energy and momentum of rotating systems; oscillations; and fluids.
What value of g should I use in AP Physics 1?
g = 9.8 m/s² (the sheet gives it). Using 10 m/s² for quick estimates is usually accepted, but show your working.
Is the equation sheet enough to pass?
No. It lists the equations but not when to use them or what the symbols mean in a given problem. The marks come from choosing the right one, explaining the physics and checking units.
