PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
Two identical competitive figure skaters, A and B, begin at rest on identical, nearly friction-free ice.
• Each skater exerts the same constant horizontal force with her skates against the ice, producing an identical constant torque about her own vertical axis.
• At the instant that force is first applied, skater A’s arms are fully extended, while skater B’s arms are held tightly against her body.
• After spinning for several revolutions, skater A suddenly pulls her arms inward until they match the position of skater B.
Ignore air resistance and any change in the applied horizontal force unless otherwise stated.
(a) At the instant the skaters first begin to turn, which skater experiences the greater magnitude of angular acceleration? Explain your reasoning without performing numerical calculations.
(b) Qualitatively describe how skater A’s angular acceleration changes, if at all, at the moment she pulls in her arms while continuing to exert the same horizontal force. Justify your answer.
(c) Immediately after pulling in her arms, skater A adjusts her push so that the horizontal force she exerts is only half as large as before. Describe how her new angular acceleration compares with the value just before she reduced the force. Provide a qualitative explanation.
(d) For the entire process described (initial push with arms extended, spinning with arms extended, pulling arms inward, and reduced push), explain whether the total work done by skater A on herself (through the skate force) is greater than, less than, or equal to the work done by skater B during the same time interval. Support your claim with clear physical reasoning.