Angular Momentum and Its Conservation
Angular momentum is defined for a particle by its position and momentum and for a rigid body by its moment of inertia and angular velocity, and it changes only when an external torque acts. A skater pulling in her arms and a gyroscope precessing are the same law seen twice.
What a learner can do afterwards
- Computes the angular momentum of a particle about a stated point and of a rigid body about its axis
- Uses conservation of angular momentum where the net external torque is zero
- Explains gyroscopic precession as the response of an angular momentum vector to a torque
1 · Read
Angular momentum measures how much rotation a thing carries. For a single particle it is position cross momentum, and only the part of the motion that circles your chosen point counts. For a rigid body on a fixed axle it is simpler: L equals I times omega. Direction matters, so L points along the axle by the right-hand rule. A net torque changes L the way a net force changes momentum. Push off centre and the spin changes; push straight through the axle and nothing happens.
Watch a skater spin with arms wide, then pull them in. Her spin rate jumps up, though nothing twisted her around. Pulling in shrinks her moment of inertia, so omega must grow to keep the product I times omega fixed. With almost no outside torque, total L stays constant before and after. The same trade explains divers tucking to spin faster. Note that her kinetic energy still rises, since her muscles do work pulling in.
A fast top refuses to fall over, and instead its axis slowly circles the vertical. This circling is called precession. Gravity still pulls on the centre of mass and still applies a torque about the tip. But the torque nudges the direction of the L vector sideways instead of shrinking it, and those nudges add up to a steady sweep. Gyroscopes in ships, planes, and phones use exactly this response to sense turns.
Run every spin problem through one checklist. Name the point you measure L about. Add up outside torques about that point. If none act, set L before equal to L after and solve. Use it for skaters pulling in, divers tucking, and stars collapsing. Never assume L is conserved when an outside twist is present.
Angular momentum is I times omega for a spinning body, it stays fixed when no outside torque acts, and a torque on a gyroscope turns the spin axis sideways.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.