angular momentum
Angular momentum is spin's version of momentum — a single number capturing how much rotation an object has locked in, and how stubbornly it keeps turning. A spinning top stays upright, a gyroscope resists being tipped, a bicycle stays balanced while rolling: all of these are angular momentum showing its stubbornness. Where ordinary momentum measures how hard it is to stop something moving, angular momentum measures how hard it is to stop something spinning.
For a rigid object turning about a fixed axis, angular momentum is L = I omega — the moment of inertia times the angular velocity — which is the exact echo of linear momentum p = m v. Its units are kilogram metres squared per second (kg m^2/s). For a single particle it is L = r x p, whose magnitude is r m v sin theta: a mass m moving with speed v at distance r from a chosen point, with theta the angle between them. Like its cousins, angular momentum is a vector, pointing along the axis by the right-hand rule.
Angular momentum earns its fame because it is conserved: with no net external torque, an object's total angular momentum cannot change. That single fact powers a skater's spin-up, a diver's somersault, the sweep of the planets, and the rapid spin of a collapsing star. It is one of the deepest bookkeeping rules in physics.
A disk with I = 0.09 kg m^2 spinning at omega = 20 rad/s carries angular momentum L = I omega = 0.09 x 20 = 1.8 kg m^2/s. To stop it in a given time takes a torque equal to that L divided by the time.
L = I omega is the rotational twin of p = m v.
Angular momentum is defined about a chosen axis or point; the same motion has different L about different points. It is a distinct quantity from linear momentum, not a version of it.