A competitive figure skater begins a spin with her arms fully extended and her body…
PHYSICS · Multi-part · AP · Physics C: Mechanics · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A competitive figure skater begins a spin with her arms fully extended and her body approximated as a rigid cylinder of rotational inertia I0 about the vertical axis through her center. Embedded in each hand is a small 0.40kg mass held at a distance r0 from the axis. The skater’s initial angular speed is ω0. After a brief interval she draws both arms inward so that each mass is now at a reduced distance rf from the spin axis. Neglect all external torques on the skater–mass system during the interval.
Answer the following questions about the interval during which the arms are drawn inward.
(a) Describe qualitatively how the total rotational inertia of the system changes as the arms move from the initial to the final position.
(b) Explain, without performing numerical calculations, how the skater’s angular speed is affected by the change described in part (a). Be sure to reference relevant physical quantities in your explanation.
(c) After the arms are fully drawn in, compare the rotational kinetic energy of the system with its initial value. Provide a reasoned argument for any increase or decrease.