A spinning skater draws in her outstretched arms thereby reducing her moment of inertia by a factor of 2. Determine the ratio of her final kinetic energy to her initial kinetic energy.
A)0.5
B)1
C)2
D)4
E)16

Question

Quizplus · Accepted Answer

According to the law of conservation of angular momentum, the product of moment of inertia and angular velocity must remain constant. As moment of inertia reduces by a factor of 2, angular velocity doubles to maintain angular momentum. Kinetic energy of a rotating object is given by (1/2)*I*w^2. As w doubles, kinetic energy increases by a factor of 2^2 = 4. Therefore, the ratio of final to initial kinetic energy is 4/1 = 4, which corresponds to option (C).

A Spinning Skater Draws in Her Outstretched Arms Thereby Reducing