Unit 6: Energy and Momentum of Rotating Systems
What this unit is about
A figure skater pulls in her arms and spins faster. A soup can beats an empty can down a ramp. A satellite circles the Earth for years without an engine. All three follow two big rules you already know from Units 3 and 4, now applied to things that spin: energy is conserved and momentum is conserved.
Unit 5 told you why things start spinning (torque). This unit tells you how much energy a spin holds, how torque does work, and why a spin keeps going.
Exam weight and what you need first
On the AP Physics 1 exam (course and exam description effective fall 2024), Unit 6 is about 5 % to 8 % of the multiple choice score. Its ideas also show up inside free response questions about energy and momentum.
Before you start, be comfortable with: angular velocity ω and angular acceleration α, torque τ = rF sin θ, and rotational inertia I (Unit 5); kinetic and potential energy and work (Unit 3); momentum and impulse (Unit 4).
| Moving in a line | Spinning |
|---|---|
| Kinetic energy ½mv² | Rotational kinetic energy ½Iω² |
| Work W = FΔx (force along the motion) | Work W = τΔθ |
| Momentum p = mv | Angular momentum L = Iω (point mass: L = mvr⊥) |
| Impulse FΔt = Δp | Angular impulse τΔt = ΔL |
| No net external force: p is conserved | No net external torque: L is conserved |
Topics
- 6.1 Rotational Kinetic Energy
A spinning potter's wheel stores energy: K = ½Iω². Mass far from the axis stores more.
- 6.2 Torque and Work
Pushing a merry-go-round: a torque turning through an angle does work, W = τΔθ, and that work becomes spin energy.
- 6.3 Angular Momentum and Angular Impulse
L = Iω for a spinning object, L = mvr⊥ for a moving point. A torque acting for a time changes L: τΔt = ΔL.
- 6.4 Conservation of Angular Momentum
The skater pulls in her arms: I drops, ω jumps, L stays the same. Clay dropped on a turntable slows it down.
- 6.5 Rolling
The can race: v = ωR, and the energy splits between moving and spinning. Less spin share means a faster finish.
- 6.6 Motion of Orbiting Satellites
Circular and elliptical orbits, orbital speed and period, energy of a satellite, and escape speed.
Play and practice
- Unit 6 games: the rolling race, the skater spin challenge, the orbit launcher and the rolling energy bar puzzle. Each has levels and a score.
- Unit 6 practice set: a full-length AP-style set with multiple choice and free response questions, all with hidden worked answers.
How to use this unit: read the story and the idea, play with the lab (use Predict first), try the examples before opening the solution, then do the practice. Finish with the games and the practice set.