Inside This Unit: The Full Breakdown
This unit covers rotational kinetic energy, the total energy of rolling bodies, angular momentum L = Iω, and its conservation when no external torque acts.
Why it matters
Angular momentum conservation explains a range of phenomena (skaters, collisions with rotation) and pairs with energy methods for rolling problems.
Key concepts
- Rotational kinetic energy is ½Iω²; rolling bodies have ½mv² + ½Iω².
- Angular momentum L = Iω; net torque equals dL/dt.
- With no external torque, L is conserved (I₁ω₁ = I₂ω₂).
- Rotational collisions conserve L but may lose kinetic energy.
Rotational Energy and Rolling
A rotating body stores kinetic energy ½Iω²; a rolling body combines translational and rotational kinetic energy. Because energy splits according to I, a solid disk beats a hoop down a ramp. Use v = Rω in energy conservation for rolling.
Angular Momentum and Its Conservation
Angular momentum is L = Iω (and τ = dL/dt). With no external torque it is conserved: a skater pulling in their arms reduces I and spins faster. Rotational collisions (clay sticking to a disk) conserve angular momentum while losing kinetic energy.
AP exam tip
When I changes with no external torque, conserve L (I₁ω₁ = I₂ω₂) — do not assume rotational kinetic energy is also conserved; it usually is not.
Connections to other units
- Unit 3: Energy methods extend to rotation here.
- Unit 4: Angular momentum mirrors linear momentum conservation.
