Angular momentum is conserved. Figure skaters — and satellites — know this. Unit 3 and Unit 4's tools come back, rebuilt for anything that spins.
Episode Guide — Season 6
K = ½mv² had a rotational twin waiting all along: K_rot = ½Iω². A rolling object carries both kinds at once.
Force times distance becomes torque times angle. The rotational work-energy theorem falls straight out of the same logic as Unit 3.
L = r × p for a particle, or L = Iω for a rigid body — two ways of describing the same conserved quantity that keeps a spinning system spinning.
Zero net external torque means L never changes — even if I does. That's how a figure skater speeds up just by pulling their arms in.
Rolling without slipping links v_cm and ω exactly. The instant a system slips, that link breaks — and friction starts stealing energy.
Circular orbits keep everything constant; elliptical ones trade kinetic and potential energy back and forth while angular momentum holds steady. Escape velocity is just the point where total energy hits zero.