An ice skater spins at 2.5 rev/s when his arms are extended.He draws his arms in and spins at 6.0 rev/s.By what factor does his moment of inertia change in the process?
A)2.4
B)1.0
C)0.42
D)0.12

Question

Quizplus · Accepted Answer

The moment of inertia of a system is given by the equation I=mr^2, where m is the mass and r is the radius of gyration. When the ice skater draws his arms in, his mass remains the same, but his radius of gyration decreases. Since the moment of inertia is proportional to the square of the radius of gyration, the moment of inertia decreases by a factor of (1/2.5)^2/(1/6)^2, which simplifies to 0.42. Therefore, the correct answer is C.

An Ice Skater Spins at 2