AP Physics 1 Unit 3: Work, Energy, and Power Notes

Introduction

Energy accounting connects a system’s initial and final states by tracking stored energy, work across the boundary, and conversion into nonmechanical forms.

Begin every energy argument by naming the system, reference frame, and zero of potential energy. Those choices determine whether gravity or a spring appears as potential energy inside the system or as work done from outside it. The prediction cannot change when the accounting convention changes consistently.

Work transfers energy through a force acting over displacement. Kinetic and potential energy describe states; power describes the rate of transfer. A reliable solution inventories energy at two states, identifies every boundary transfer, and checks that the final ledger balances.

Mass and frame-labeled speed

translational kinetic energy

Force parallel to displacement

work and change in kinetic energy

Conservative interaction and configuration

potential energy

System boundary and transfers

energy conservation

Energy transferred per time

power

Current exam guidance: Aligned to the current 2026–27 AP Physics 1 framework, with algebra-based modeling, experimental reasoning, and explicit assumptions.

3.1

Translational Kinetic Energy

How do mass, speed, and reference frame determine translational kinetic energy?

Short answer

In a stated frame, translational kinetic energy is $K=\tfrac12mv^2$ ; it grows linearly with mass, quadratically with speed, and never carries a direction.

Know firstVelocity in a reference frame · Mass · Quadratic proportionality

Speed sets the energy scale

Choose one object as the system and measure its velocity in a named inertial frame. Translational kinetic energy depends on speed, the magnitude of velocity. Reversing direction leaves $K$ unchanged because the velocity is squared. Doubling mass doubles $K$ , while doubling speed multiplies it by four. This makes speed changes especially important in energy comparisons.

Kinetic energy is a scalar but is not frame invariant. A cart moving at $3\ \mathrm{m/s}$ relative to the floor is stationary in a frame moving alongside it, so the two frames assign different kinetic energies. Initial and final values in one energy equation must come from the same frame. Rotational motion and microscopic thermal motion require separate energy stores.

Physics model

Kinetic energy grows with speed squared

Change speed and compare the velocity arrow with the quadratic rise in translational kinetic energy.

Speed5 m/s

Speed: 5 m/s
Momentum magnitude: 10 kg·m/s
Kinetic energy: 25 J

speedkinetic-energy barreference frame

K=\tfrac12mv^2

Read this figure without the graphic

Change speed and compare the velocity arrow with the quadratic rise in translational kinetic energy. The table below states the model assumptions and relationships without relying on color or motion.

Quantity	Meaning
Mass	2 kg
Speed doubled	Kinetic energy becomes four times as large
Frame	Speed and kinetic energy are frame dependent

Read the equation as a state relation

System: One object represented by its center-of-mass translation.
Frame: A single inertial frame with velocity measured along a declared axis.
Assumptions: Mass is constant and internal rotation is excluded.
Givens: $m$ and frame-labeled speed $|v|$ .

Square the signed velocity, so opposite directions give the same value.
Multiply by mass and one half.
Use one frame for every compared state.

Result

K=\frac{1}{2}mv^2

Units:

\mathrm{kg\,m^2/s^2}=\mathrm J

Boundary cases

$v=0$ gives $K=0$ in that frame.
Changing frame can change $v$ and therefore $K$ .

Kinetic energy equals one half mass times speed squared and is nonnegative.

Compare kinetic-energy states

Label the reference frame.
Form a ratio before substituting numbers when only factors change.
Use speed rather than signed velocity in the magnitude calculation.
Separate translational energy from rotation or internal energy.

Test the square-speed relationship

Does measured cart kinetic energy vary with the square of speed?

Variables: Independent: signed cart velocity; response: calculated $K$ ; controls: cart mass, track, and reference frame.
Apparatus: Low-speed cart, level track, photogates, balance, and catch stop.
Procedure boundary: Use instructor-approved speeds and keep the track end guarded.
Uncertainty: Propagate mass and timing uncertainty; speed uncertainty contributes twice fractionally because $v$ is squared.

Test the square-speed relationship lab dataset
Mass (kg)	Velocity (m/s)	Kinetic energy (J)
2	-3	9
2	0	0
2	3	9

Provided accessible table

Test the square-speed relationship accessible table
Mass kg	Velocity m/s	K J
2	-3	9
2	0	0
2	3	9

Keep these three ideas

Kinetic energy depends on speed squared.
Direction reversal does not make $K$ negative.
State the frame and exclude uncounted energy stores.

Work, Energy, and Power