2/15/202111.3 Conservation of Angular Momentum – University Physics Volume 11/2811 Angular Momentum11.3 Conservation of AngularMomentumLearning ObjectivesBy the end of this section, you will be able to:Apply conservation of angular momentum to determine the angular velocity of a ro‐tating system in which the moment of inertia is changingExplain how the rotational kinetic energy changes when a system undergoes changesin both moment of inertia and angular velocity
2/15/202111.3 Conservation of Angular Momentum – University Physics Volume 12/28So far, we have looked at the angular momentum of systems consisting of point particles and rigidbodies. We have also analyzed the torques involved, using the expression that relates the externalnet torque to the change in angular momentum,(Figure). Examples of systems that obey thisequation include a freely spinning bicycle tire that slows over time due to torque arising fromfriction, or the slowing of Earth’s rotation over millions of years due to frictional forces exertedon tidal deformations.However, suppose there is no net external torque on the system,In this case,(Figure)becomes thelaw of conservation of angular momentum.Law of Conservation of Angular MomentumThe angular momentum of a system of particles around a point in a fixed inertial reference frameis conserved if there is no net external torque around that point:orNote that thetotalangular momentumis conserved. Any of the individual angular momenta can change as long as their sum remainsconstant. This law is analogous to linear momentum being conserved when the external force on asystem is zero.As an example of conservation of angular momentum,(Figure)shows an ice skater executing aspin. The net torque on her is very close to zero because there is relatively little friction betweenher skates and the ice. Also, the friction is exerted very close to the pivot point. Bothare small, so
2/15/202111.3 Conservation of Angular Momentum – University Physics Volume 13/28is negligible. Consequently, she can spin for quite some time. She can also increase her rate ofspin by pulling her arms and legs in. Why does pulling her arms and legs in increase her rate ofspin? The answer is that her angular momentum is constant, so thatorwhere the primed quantities refer to conditions after she has pulled in her arms and reduced hermoment of inertia. Becauseis smaller, the angular velocitymust increase to keep the angular momentum constant.