AP Physics C: Mechanics Unit 3 Cheatsheet: Work, Energy, and Power

Start with the first 3 sections of the Unit 3 one-page cheatsheet below. The full sheet is a PDF you can print.

Kinetic Energy & Work Basics

Translational Kinetic Energy

K = ½mv² (scalar, always ≥ 0)
Frame-dependent: different observers measure different K

Work Definition

Energy transferred into/out of system by a force over distance
Scalar: can be positive, negative, or zero
Sign depends on angle between force and displacement

Work Calculation (Constant Force)

W = F‖d = Fd cos θ
Only parallel component of force does work
Perpendicular force changes direction, not kinetic energy

Power: Rate of Energy Transfer

Definitions

Power = rate of energy change with time
Average power: P_avg = ΔE/Δt = W/Δt
Instantaneous power: P_inst = dW/dt

Constant Force Formula

P_inst = F‖v = Fv cos θ
Only parallel component of force contributes
Power depends on both force and velocity

Units & Interpretation

Watts (W) = Joules/second = kg·m²/s³
High power = fast energy transfer
Same work done faster = higher power

Quick Reference: Equations & Relationships

Quantity	Equation
Kinetic Energy	K = ½mv²
Work (constant F)	W = Fd cos θ
Work (variable F)	W = ∫F·dr
Work-Energy	ΔK = ΣW
Spring PE	U_s = ½k(Δx)²
Gravity PE (surface)	ΔU_g = mgΔy
Gravity PE (general)	U_g = −Gm₁m₂/r
Force from PE	F_x = −dU/dx
Mechanical Energy	E = K + U
Avg Power	P_avg = W/Δt
Inst Power	P = Fv cos θ

The rest of the Unit 3 sheet

6 more sections are on the one-page PDF:

Work-Energy Theorem
Equilibrium from Potential Energy Graphs
Mechanical Energy Conservation
Variable Force & Integration
Potential Energy & Conservative Forces
Problem-Solving Strategy

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Unit 3: Work, Energy, and Power on one page, aligned to the 2026-2027 course. Made and checked by the Fiveable Content Team.

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