L=Iω is conserved when no external torque acts.
L=Iω for a rigid body (r×mv for particles). With no external torque L is conserved, so reducing I increases ω. This explains figure skaters spinning faster and the stability of satellites.
A skater pulling in arms halves I and doubles the spin rate.
Angular momentum is conserved when no external torque acts, which explains figure skating spins and planetary motion.
L=Iω is conserved when no external torque acts.
Angular momentum is conserved when no external torque acts, which explains figure skating spins and planetary motion.
Angular momentum stays constant, and bringing mass closer to the axis reduces the moment of inertia, so the angular velocity rises.
Only if the net external torque is zero. Friction or external moments change it.
Typical applications include explaining why a diver spins faster when tucked in, predicting the speed change of a rotating platform when a person moves inward and analysing the spin of a satellite after a deployment event.
Study "Mass moment of inertia" first (topic 37 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
dL/dt = net torque. Vector with direction along the axis. Conserved in central force fields.
A skater pulling in arms halves I and doubles the spin rate.
The next topic is "Gyroscopic effects", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 38 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.