When a massive star dies, gravity causes its radius to contract quickly from the size of a giant star (R_i= 8.0x10^8m) to roughly the size of Oahu...

When a massive star dies, gravity causes its radius to contract quickly from the size of a giant star (R_i= 8.0x10^8m) to roughly the size of Oahu (R_f= 4.0x10^4m), creating a very dense object known as a "neutron star." The initial giant star rotated with a period of 30 days, while the final neutron star rotates much faster. Assume that both before and after collapse, the star is a solid, uniform-density sphere, rotating like a rigid body about its center. Also assume that the mass of the star (M=5.0x10^30 kg) remains constant during collapse.a) find the final rotation period of the neutron star.b) find the increase in kinetic energy of the star, as a result of its contraction.c) calculate triangle (U_gr) for the star's contraction