As an ice skater begins a spin, his angular speed is 3.17 . after pulling in his arms, his angular speed increases to 5.96 . find the ratio of the skater's final moment of inertia to his initial moment of inertia.

The ratio is 0.53

Explanation:

There aren't external torques on the ice skater because we can assume ice surface frictionless and there're not external forces, that implies angular moment is conserved so it has the same value before and after him pulling his arms. Angular momentum is the product between angular velocity (ω) and moment of inertia (I).

The initial angular moment is:

(1)

and final angular moment is:

(2)

Because conservation of angular moment we can equate (1) and (2):

rearranging the expression:

So, the ratio of the skater's final moment of inertia to his initial moment of inertia is: