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AP Physics 1 formula map
Every unit of the current AP Physics 1 course in one place, with what each equation is for. Print it, or choose "Save as PDF" in the print dialog.
UNIT 1Kinematics
| v = v₀ + at | velocity after time t (constant a) |
| x = x₀ + v₀t + ½at² | position after time t |
| v² = v₀² + 2a(x − x₀) | no time needed |
| v̄ = Δx / Δt | average velocity |
| ā = Δv / Δt | average acceleration |
| ay = −g, ax = 0 | projectiles: treat x and y separately |
UNIT 2Force & translational dynamics
| ΣF = ma | Newton's 2nd law (per axis) |
| Fg = mg | weight near Earth's surface |
| Fg = Gm₁m₂ / r² | universal gravitation |
| |Ff| ≤ μs|FN| | static friction (up to a max) |
| |Ff| = μk|FN| | kinetic friction |
| Fs = −kΔx | spring force (Hooke's law) |
| ac = v² / r | centripetal acceleration |
| xcm = Σmixi / Σmi | centre of mass |
UNIT 3Work, energy & power
| K = ½mv² | translational kinetic energy |
| W = F∥d = Fd cos θ | work by a constant force |
| Wnet = ΔK | work–energy theorem |
| ΔUg = mgΔy | gravitational PE near Earth |
| UG = −Gm₁m₂ / r | gravitational PE (general) |
| Us = ½k(Δx)² | spring potential energy |
| P = ΔE / Δt | average power |
| P = F∥v | instantaneous power |
UNIT 4Linear momentum
| p = mv | momentum (a vector) |
| J = FavgΔt = Δp | impulse–momentum theorem |
| ΣF = Δp / Δt | force as the rate of change of p |
| Σpi = Σpf | conserved when there's no net external force |
| vcm = Σp / Σm | velocity of the centre of mass |
| Ki = Kf | elastic collisions only |
UNIT 5Torque & rotational dynamics
| ω = ω₀ + αt | constant angular acceleration |
| θ = θ₀ + ω₀t + ½αt² | angular position |
| ω² = ω₀² + 2α(θ − θ₀) | no time needed |
| v = rω, at = rα | linking linear and angular motion |
| τ = rF sin θ = r⊥F | torque |
| α = Στ / I | Newton's 2nd law for rotation |
| I = Σmiri² | rotational inertia |
| I′ = Icm + Md² | parallel-axis theorem |
UNIT 6Energy & momentum of rotating systems
| Krot = ½Iω² | rotational kinetic energy |
| W = τΔθ | work done by a torque |
| L = Iω | angular momentum of a rigid body |
| L = rmv sin θ | angular momentum of a point mass |
| ΔL = τΔt | angular impulse |
| vcm = rω | rolling without slipping |
| K = ½Mvcm² + ½Iω² | total KE of a rolling object |
| v = √(GM / r) | circular orbit (from Fg = mv²/r) |
UNIT 7Oscillations
| T = 1 / f | period and frequency |
| Ts = 2π√(m / k) | mass on a spring |
| Tp = 2π√(ℓ / g) | simple pendulum (small angles) |
| x = A cos(2πft) | position in SHM (starts at x = A) |
| E = ½kA² = ½mvmax² | total energy of the oscillator |
UNIT 8Fluids
| ρ = m / V | density |
| P = F⊥ / A | pressure |
| P = P₀ + ρgh | pressure at depth h |
| Fb = ρfluidVdispg | buoyant force (Archimedes) |
| A₁v₁ = A₂v₂ | continuity (flow rate is constant) |
| P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂² | Bernoulli's equation |
CONSTANTSUseful values
| g = 9.8 m/s² | free-fall acceleration near Earth (≈ 10 m/s² for estimates) |
| G = 6.67 × 10⁻¹¹ N·m²/kg² | universal gravitational constant |
| ρwater = 1000 kg/m³ | density of water |
| Patm ≈ 1.0 × 10⁵ Pa | atmospheric pressure at sea level |
Bold symbols are vectors. Always draw a diagram, choose a positive direction, and check your units.