PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
Two identical figure skaters, A and B, each of mass 60kg, stand on frictionless ice facing each other at a separation of 2.0m. Each skater may be modeled as a uniform cylinder of radius 0.30m with moment of inertia Is=3.2kgm2 about a vertical axis through the skater’s center of mass.
Skater A places her hands on Skater B’s shoulders and pushes straight outward with an average force of magnitude 120N for 0.40s. During the push, their arms remain horizontal so that the force on each acts at a distance 0.45m from the common vertical axis midway between them.
Ignore all external forces and friction with the ice. Treat each skater as a rigid body throughout the motion.
(a) Calculate the magnitude of the angular impulse delivered to Skater A about the common vertical axis during the push.
(b) Determine the magnitude and direction of the angular momentum gained by Skater B during the push.
(c) Find the final angular speed of each skater about the common vertical axis after the push ends.
(d) After the push, the skaters draw their arms inward, reducing their individual moments of inertia to 2.5kgm2 each. Calculate their new angular speeds, and explain why their directions of rotation remain unchanged.