Physics 1
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AP Physics 1 — Equations & Constants

8 sections · 46 entries · print it and keep it beside your practice sets

Algebra-based mechanics, rotation, simple harmonic motion, and fluids. Every relationship here is on the sheet you are handed on exam day, so the skill being tested is never recall — it is choosing the right line and tracking units. Practise with this open.

Practise with the sheet, not from memory. The College Board hands out its own version of this page on exam day, so nothing here is worth memorising for its own sake. What earns points is speed: knowing which section a quantity lives in, and reading off the right line without breaking your train of thought. Keep this open (or printed) for every practice set you do.

Kinematics (straight line, constant acceleration)

v
v = v₀ + a t

Velocity after time t from initial velocity v₀

x
x = x₀ + v₀ t + ½ a t²

Position after time t

v² = v₀² + 2a(x − x₀)

Velocity as a function of displacement (no t)

The go-to equation whenever the problem never mentions time.

v_avg
v_avg = (v₀ + v)/2 = Δx/Δt

Average velocity (constant a only)

Forces & Newton’s laws

a
a = ΣF/m = F_net/m

Acceleration from the net force on mass m

F_f
|F_f| ≤ μ|F_n|

Magnitude of friction from normal force F_n

Equality holds for kinetic friction; static friction is at most μ_s F_n.

F_s
|F_s| = k|x|

Spring (Hooke) force for displacement x from equilibrium

F_g
F_g = G m₁ m₂ / r²

Gravitational force between masses m₁ and m₂

g
g = F_g/m = G M / r²

Gravitational field strength

a_c
a_c = v²/r = ω² r

Centripetal acceleration in a circle of radius r

Points toward the centre. It is a required acceleration, not an extra force — never add “centrifugal force” to a free-body diagram.

Energy & power

K
K = ½ m v²

Translational kinetic energy

W
W = F d cos θ

Work done by a constant force F over displacement d

θ is the angle between force and displacement, so a force perpendicular to motion does zero work.

ΔU_g
ΔU_g = m g Δh

Change in gravitational potential energy near Earth

U_s
U_s = ½ k x²

Elastic potential energy in a spring

P
P = ΔE/Δt = F v cos θ

Average power

ΔE
ΔE_system = W_external + Q

Energy conservation for a system

Momentum & impulse

p
p = m v

Linear momentum

Δp
Δp = F_avg Δt

Impulse–momentum theorem

Σp
Σp_before = Σp_after

Conservation of momentum (no external impulse)

Rotation & torque

ω
ω = Δθ/Δt

Angular velocity; θ in radians

ω(t)
ω = ω₀ + α t

Angular velocity with constant angular acceleration

θ(t)
θ = θ₀ + ω₀ t + ½ α t²

Angular position with constant α

v, a_t
v = ω r, a_t = α r, s = θ r

Linking linear and angular motion

τ
τ = r F sin θ

Torque from force F applied at distance r

r sin θ is the lever arm — the perpendicular distance from the axis to the line of action.

α
α = Στ/I = τ_net/I

Angular acceleration from net torque

I
I = Σ m r²

Rotational inertia of point masses about an axis

K_rot
K_rot = ½ I ω²

Rotational kinetic energy

L
L = I ω

Angular momentum of a rigid body

ΔL
ΔL = τ Δt

Angular impulse

Simple harmonic motion

x(t)
x = A cos(2π f t)

Displacement of an oscillator of amplitude A

T, f
T = 1/f = 2π/ω

Period and frequency

T_s
T_s = 2π √(m/k)

Period of a mass–spring oscillator

T_p
T_p = 2π √(ℓ/g)

Period of a simple pendulum of length ℓ

Independent of mass and (for small angles) of amplitude.

Fluids

ρ
ρ = m/V

Density

P
P = F/A

Pressure from a force on area A

P(h)
P = P₀ + ρ g h

Absolute pressure at depth h below a surface at P₀

F_b
F_b = ρ_fluid V_displaced g

Buoyant force (Archimedes)

A v
A₁ v₁ = A₂ v₂

Continuity for an incompressible fluid

Bernoulli
P₁ + ρ g y₁ + ½ ρ v₁² = P₂ + ρ g y₂ + ½ ρ v₂²

Energy conservation along a streamline

Geometry & trigonometry (also supplied)

Areas
A = b h, A = ½ b h, A = π r²

Rectangle, triangle, circle

Volumes
V = ℓ w h, V = π r² ℓ, V = (4/3) π r³

Rectangular solid, cylinder, sphere

Right triangle
a² + b² = c², sin θ = a/c, cos θ = b/c, tan θ = a/b

Pythagoras and the basic ratios

# Constants & conversions

g
g = 9.8 m/s²

Free-fall acceleration near Earth’s surface

The exam sheet rounds to 9.8; 10 m/s² is fine for estimates but show the value you used.

G
G = 6.67 × 10⁻¹¹ N·m²/kg²

Universal gravitational constant

M_E
M_E = 5.97 × 10²⁴ kg

Mass of Earth

R_E
R_E = 6.37 × 10⁶ m

Radius of Earth

Practise with the sheet openExam-skill drillsCheatsheet