(100 points!)
A star of radius R1 rotates every 20 days. The star suddenly collapses to a radius R2, which is smaller by a factor of 10000 (R2=R1/10000) without losing mass.
a. What is the new angular velocity of the star? You may assume that the moment of inertia of the star is that of a solid sphere (I=(2/5)mR^2)?
b. What is the ratio of the kinetic energy before and after the collapse (KEf/KEi)?