AP Physics 1 Formula Sheet

KinematicsDynamicsCircularEnergyMomentumSimpleTorqueElectricDCWaves

AP Physics 1 Formula Sheet

All key equations organized by topic. Memorize these — the AP exam does not provide a formula sheet.

Kinematics

v = v_0 + at

Velocity after constant acceleration

v = final velocity, v₀ = initial velocity, a = acceleration, t = time

Units: v: m/s, a: m/s², t: s

x = x_0 + v_0 t + (1)/(2)at²

Position under constant acceleration

x = final position, x₀ = initial position

Units: x: m

v² = v_0² + 2aΔ x

Velocity–displacement relation (time-independent)

Δx = displacement

Units: v: m/s, a: m/s², x: m

x = ((v + v_0))/(2) · t

Average velocity × time (constant acceleration)

(v + v₀)/2 = average velocity

Units: m

Dynamics (Newton's Laws)

F_net = ma

Newton's Second Law

F_net = net force, m = mass, a = acceleration

Units: F: N, m: kg, a: m/s²

F_friction = μ N

Friction force (kinetic or maximum static)

μ = coefficient of friction, N = normal force

Units: N

F_g = mg

Weight (gravitational force near Earth's surface)

g = 9.8 m/s² ≈ 10 m/s² (near Earth)

Units: N

Circular Motion & Gravitation

a_c = (v²)/(r)

Centripetal acceleration

a_c = centripetal acceleration, v = speed, r = radius

Units: m/s²

F_c = (mv²)/(r)

Centripetal force (net inward force required)

F_c = centripetal force

Units: N

F_g = (Gm_1 m_2)/(r²)

Newton's Law of Universal Gravitation

G = 6.67×10⁻¹¹ N·m²/kg², m₁, m₂ = masses, r = distance between centers

Units: N

g = (GM)/(r²)

Gravitational field / surface gravity

M = mass of planet, r = distance from center

Units: m/s²

T² = (4π²)/(GM) r³

Kepler's Third Law (orbital period)

T = orbital period, r = orbital radius, M = mass of central body

Units: T: s, r: m

Energy

W = Fd\cosθ

Work done by a constant force

W = work, F = force magnitude, d = displacement, θ = angle between F and d

Units: J

KE = (1)/(2)mv²

Kinetic energy

KE = kinetic energy, m = mass, v = speed

Units: J

PE_g = mgh

Gravitational potential energy

h = height above reference point

Units: J

PE_spring = (1)/(2)kx²

Elastic potential energy (spring)

k = spring constant, x = compression/stretch from equilibrium

Units: J

P = (W)/(t) = Fv

Power

P = power, W = work, t = time

Units: W (watts)

W_net = Δ KE

Work-Energy Theorem

W_net = net work done on object, ΔKE = change in kinetic energy

Units: J

Momentum & Impulse

p = mv

Linear momentum

p = momentum, m = mass, v = velocity

Units: kg·m/s

J = FΔ t = Δ p

Impulse-Momentum Theorem

J = impulse, F = average force, Δt = time interval, Δp = change in momentum

Units: N·s = kg·m/s

p_total = constant (isolated system)

Conservation of Momentum

Valid when net external force = 0

Units: kg·m/s

Simple Harmonic Motion

T_spring = 2π√((m)/(k))

Period of a mass-spring system

T = period, m = mass, k = spring constant

Units: s

T_pendulum = 2π√((L)/(g))

Period of a simple pendulum (small angles)

L = pendulum length, g = gravitational field

Units: s

x = A\cos\left((2π t)/(T)\right)

Position in SHM (released from amplitude)

x = position, A = amplitude, T = period

Units: m

v_max = A√((k)/(m))

Maximum speed (at equilibrium)

v_max = maximum speed, A = amplitude

Units: m/s

E = (1)/(2)kA²

Total mechanical energy in SHM

E = total energy, k = spring constant, A = amplitude

Units: J

Torque & Rotational Motion

τ = rF\sinθ

Torque

τ = torque, r = lever arm length, F = force, θ = angle between r and F

Units: N·m

Σ τ = Iα

Newton's Second Law for Rotation

Στ = net torque, I = rotational inertia (moment of inertia), α = angular acceleration

Units: N·m

L = Iω

Angular momentum

L = angular momentum, I = rotational inertia, ω = angular velocity

Units: kg·m²/s

L = constant (no external torque)

Conservation of Angular Momentum

Valid when net external torque = 0

Units: kg·m²/s

I_point = mr²

Rotational inertia of a point mass

I = moment of inertia, m = mass, r = distance from axis

Units: kg·m²

Electric Charge & Force

F_E = (kq_1 q_2)/(r²)

Coulomb's Law (electric force between charges)

F_E = electric force, k = 9×10⁹ N·m²/C², q₁, q₂ = charges, r = separation

Units: N

k = 9 × 10^9 N·m²/C²

Coulomb's constant

k = electrostatic constant

Units: N·m²/C²

E = (F)/(q) = (kq)/(r²)

Electric field

E = electric field strength, F = force on test charge q

Units: N/C

DC Circuits

V = IR

Ohm's Law

V = voltage (potential difference), I = current, R = resistance

Units: V, A, Ω

P = IV = I² R = (V²)/(R)

Electrical power

P = power

Units: W

R_series = R_1 + R_2 + \ldots

Resistors in series

Same current through each; voltages add

Units: Ω

(1)/(R_parallel) = (1)/(R_1) + (1)/(R_2) + \ldots

Resistors in parallel

Same voltage across each; currents add

Units: Ω

Waves & Sound

v = fλ

Wave speed

v = wave speed, f = frequency, λ = wavelength

Units: v: m/s, f: Hz, λ: m

f_obs = f_src · \fracv ± v_obsv ∓ v_src

Doppler Effect

v = wave speed, v_obs = observer speed, v_src = source speed. Use + for approaching, − for receding

Units: Hz

f_n = (nv)/(2L) (n = 1, 2, 3, \ldots)

Standing waves: open tube or string fixed at both ends

f_n = nth harmonic frequency, L = tube/string length

Units: Hz

f_n = (nv)/(4L) (n = 1, 3, 5, \ldots)

Standing waves: closed tube (one closed end)

Only odd harmonics; n must be odd

Units: Hz

Important Constants

Gravitational acceleration (near Earth)

g = 9.8 m/s² ≈ 10 m/s²

Universal gravitational constant

G = 6.67 × 10⁻¹¹ N·m²/kg²

Coulomb's constant

k = 9 × 10⁹ N·m²/C²

Speed of sound in air (room temp)

v_sound ≈ 343 m/s

Mass of electron

m_e = 9.11 × 10⁻³¹ kg

Elementary charge

e = 1.6 × 10⁻¹⁹ C

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