Physiworld · AP Physics 1 equation sheet, explained · www.physiworld.com/ap-physics-1/formula-sheet/
AP Physics 1 unit map AP Physics 1The equation sheet, explained
The equations of AP Physics 1, grouped by the eight units of the course, with what each one says and the SI unit of each symbol. Each equation links the Physiworld lesson that teaches it; lessons open with a free account. The revision notes explain each topic with worked examples.
All of these are on the exam's reference sheet. The College Board hands out its equation table in the exam. It names the symbols but not when each equation applies, which is what the meanings here are for.
Unit 1 · Kinematics
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
vx = vx0 + axt | Velocity after a time t at constant acceleration.
| Dynamics 5 · Equations of Motion |
x = x0 + vx0t + ½axt2 | Position after a time t at constant acceleration.
| Dynamics 5 · Equations of Motion |
vx2 = vx02 + 2ax(x − x0) | Velocity and displacement at constant acceleration, without the time. Use each component separately for projectiles. | Dynamics 9 · Projectiles |
Unit 2 · Force and translational dynamics
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
xcm = ΣmixiΣmi | Center of mass: the mass-weighted average position of a system.
| Dynamics 7 · Centre of Gravity |
asys = ΣFmsys = Fnetmsys | Newton's second law for a system: net external force over total mass.
| Dynamics 1 · Newton’s Second Law |
|Fg| = Gm1m2r2 | Newton's law of gravitation: an inverse-square attraction between any two masses.
| Gravity 2 · Gravity and Distance |
|Ff| ≤ |μFN| | Friction is at most μ times the normal force; kinetic friction equals μₖF_N, static friction adjusts up to μₛF_N.
| Dynamics 9 · Friction |
Fs = −kΔx | Hooke's law: an ideal spring pulls back in proportion to its stretch, opposite to it.
| Dynamics 6 · Hooke’s Law |
ac = v2r | Centripetal acceleration of uniform circular motion, pointing to the center.
| Dynamics 8 · What Sets the Force |
Unit 3 · Work, energy and power
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
K = ½mv2 | Translational kinetic energy.
| Dynamics 3 · Kinetic Energy |
W = F∥d = Fd cos θ | Only the force component along the displacement does work.
| Dynamics 3 · Work Done |
ΔK = ΣWi = ΣF∥,idi | Work-energy theorem: the net work done on an object equals its change in kinetic energy. | Dynamics 3 · Work Done |
Us = ½k(Δx)2 | Elastic potential energy stored in an ideal spring.
| Dynamics 6 · Elastic Potential Energy |
UG = −Gm1m2r | Gravitational potential energy of two masses, zero when they are infinitely far apart. | Gravity 9 · Beyond mgh |
ΔUg = mgΔy | Change in gravitational potential energy near Earth's surface.
| Dynamics 3 · Energy Conservation |
Pavg = WΔt = ΔEΔt | Average power: energy transferred per unit time.
| Dynamics 3 · Power |
Pinst = F∥v = Fv cos θ | Instantaneous power delivered by a force on a moving object. | Dynamics 3 · Power |
Unit 4 · Linear momentum
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
p = mv | Momentum is a vector, in the direction of the velocity.
| Dynamics 2 · Momentum |
Fnet = ΔpΔt = mΔvΔt = ma | Net force is the rate of change of momentum. | Dynamics 2 · Impulse |
J = FavgΔt = Δp | Impulse equals the change in momentum; it is the area under a force-time graph.
| Dynamics 2 · Impulse |
vcm = ΣpiΣmi = ΣmiviΣmi | The center of mass moves at constant velocity when no net external force acts, which is momentum conservation. | Dynamics 2 · Conservation of Momentum |
Unit 5 · Torque and rotational dynamics
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
ω = ω0 + αt | Angular velocity at constant angular acceleration.
| Dynamics 10 · Rotational Kinematics |
θ = θ0 + ω0t + ½αt2 | Angular position at constant angular acceleration.
| Dynamics 10 · Rotational Kinematics |
ω2 = ω02 + 2α(θ − θ0) | Angular velocity and angle at constant angular acceleration, without the time. | Dynamics 10 · Rotational Kinematics |
v = rω aT = rα | Linear speed and tangential acceleration of a point at radius r.
| Dynamics 10 · Rotational Kinematics |
τ = r⊥F = rF sin θ | Torque: force times its lever arm.
| Dynamics 10 · Torque and Rotational Inertia |
I = Σmiri2 I′ = Icm + Md2 | Rotational inertia, and the parallel-axis theorem for an axis a distance d from the center of mass.
| Dynamics 10 · Torque and Rotational Inertia |
αsys = ΣτIsys = τnetIsys | Newton's second law for rotation. | Dynamics 10 · Torque and Rotational Inertia |
Unit 6 · Energy and momentum of rotating systems
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
K = ½Iω2 | Rotational kinetic energy; a rolling object has this plus ½mv². | Dynamics 10 · Rolling and Rotational Energy |
W = τΔθ | Work done by a constant torque through an angle. | Dynamics 10 · Rolling and Rotational Energy |
L = Iω L = rmv sin θ | Angular momentum of a rotating body, and of a point mass about an axis.
| Dynamics 10 · Angular Momentum |
ΔL = τΔt | Angular impulse: with no net external torque, angular momentum is conserved. | Dynamics 10 · Angular Momentum |
Δxcm = rΔθ | Rolling without slipping: the center moves one radius of arc per radian turned. | Dynamics 10 · Rolling and Rotational Energy |
Unit 7 · Oscillations
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
T = 1f | Period is the time for one full cycle.
| Waves 8 · Period of a Spring |
Ts = 2π√(mk) | Period of a mass on a spring; it does not depend on the amplitude. | Waves 8 · Period of a Spring |
Tp = 2π√(ℓg) | Period of a simple pendulum at small angles; mass does not matter.
| Waves 8 · The Pendulum |
x = A cos(2πft) or A sin(2πft) | Position in simple harmonic motion; which one depends on where the motion starts.
| Waves 8 · Graphs of SHM |
Unit 8 · Fluids
| Equation | What it says, symbols and units | Lesson |
|---|---|---|
ρ = mV | Density: mass per unit volume.
| Fluids 1 · Density |
P = F⊥A | Pressure: perpendicular force per unit area. 1 atm = 1.0 × 10⁵ Pa.
| Fluids 3 · Pressure |
P = P0 + ρgh Pgauge = ρgh | Absolute pressure at depth h below a surface at pressure P₀; gauge pressure leaves P₀ out. | Fluids 6 · Total Pressure |
Fb = ρVg | Buoyant force equals the weight of the fluid displaced (ρ and V of the fluid displaced). | Fluids 2 · Volume, Not Weight |
A1v1 = A2v2 | Continuity: an ideal fluid speeds up where the pipe narrows. | Fluids 4 · Continuity |
P1 + ρgy1 + ½ρv12 = P2 + ρgy2 + ½ρv22 | Bernoulli's equation: energy per unit volume is conserved along a flow. | Fluids 4 · Bernoulli |
Written in Physiworld's own words; grouped by the course's units, the same topics as the College Board's equation table.
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