A figure skater of total mass is spinning on low-friction ice with arms fully extended
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A figure skater of total mass M is spinning on low-friction ice with arms fully extended. For times t<0 her moment of inertia about the spin axis is a constant I0 and her angular speed is a constant ω0. At t=0 she begins to pull her arms inward smoothly, completing the motion at t=2s, after which her arms remain against her body.
A motion-tracking device records her angular speed ω(t) versus time. The recorded graph is described as follows:
• For t<0, ω(t)=ω0 (a horizontal line).
• From t=0 to t=2s, ω(t) rises smoothly and monotonically, reaching a constant value of 3ω0 at t=2s.
• For t>2s, ω(t)=3ω0 (another horizontal line).
Assume the vertical axis of rotation remains fixed and external torques are negligible.
(a) Sketch or describe qualitatively the corresponding graph of the skater’s moment of inertia I(t) versus time. Indicate its value before, during, and after the arm-pulling motion, and explain the key features of your graph.
(b) During the interval 0<t<2s does the skater do positive work, negative work, or zero work on the system consisting of herself and the ice? Justify your answer.
(c) The net external torque on the system is essentially zero throughout the motion, yet the rotational kinetic energy changes. Explain how this change is possible without violating the conservation of angular momentum.