Physics · Circular motion. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Moment of inertia I does for rotation what mass does for straight-line motion: it measures how hard it is to change the rotation of a body. It depends on the mass and on how far that mass lies from the axis. Mass far from the axis gives a large I, so a hoop has a larger I than a disc of the same mass and radius.
Angular momentum is L = Iω. If no external torque acts, L stays constant. When a spinning skater pulls in her arms, I falls, so ω rises.
A rotating body has rotational kinetic energy. A body rolling down a slope shares its lost potential energy between linear and rotational kinetic energy, so it is slower than a body sliding without friction.
When the skater pulls her arms in, angular momentum stays the same but rotational kinetic energy does not. It increases, because she does work in pulling her arms inwards.
Answer: About 2.2 m s−1
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