PHYS 2211 Module 11.3

Conservation of Angular Momentum

11.3 Conservation of Angular Momentum

Learning Objectives

By the end of this section, you will be able to:

Apply conservation of angular momentum to determine the angular velocity of a rotating system in which the moment of inertia is changing
Explain how the rotational kinetic energy changes when a system undergoes changes in both moment of inertia and angular velocity

Law of conservation of angular momentum

The angular momentum of a system of particles around a point in a fixed inertial reference frame is conserved if there is no net external torque around that point:

Practice!

Practice 11.3.1
A figure skater stands on one spot on the frictionless ice and spins around with her arms extended. When she pulls in her arms, she reduces her rotational inertia and her angular speed …
(a) increases
(b) decreases
(c) remains the same

Practice 11.3.2
Compared to her initial rotational kinetic energy, her rotational kinetic energy after she has pulled in her arms must be …
(a) the same
(b) larger because she is rotating faster
(c) smaller because her rotational inertia is smaller.

Practice 11.3.3
If the polar ice caps were to melt completely due to global warming, the melted ice would redistribute itself over the earth. This change would cause the length of the day (the time needed for the earth to rotate once on its axis) to … (Hint: Use angular momentum ideas. Assume that the sun, moon, and planets exert negligibly small torques on the earth.)
(a) increase
(b) decrease
(c) remain the same

Discuss!

You have been asked to help evaluate a proposal to build a device to determine the speed of hockey pucks shot along the ice. The device consists of a rod which rests on the ice and is fastened to the ice at one end so that it is free to rotate horizontally. The free end of the rod has a small, light basket which will catch the hockey puck. The puck slides across the ice perpendicular to the rod and is caught in the basket which is initially at rest. The rod then rotates. The designers claim that knowing the length of the rod, the mass of the rod, the mass of the puck, and the rotational speed of the rod and puck, you can determine the speed of the puck as it moved across the ice.