a rotating star collapses under the influence of gravitational forces to form a

Question

a rotating star collapses under the influence of gravitational forces to form a pulsar. The radius of the star after collapse is 1.0e-4 times the radius before collapse.There is no charge in mass.In both cases the mass of the star is uniformly distributed in a spherical shape find the ratios of a) angular momentum, b) angular velocity c) rotational kinetic energy of the star after collision to the values before collapses and d) if the period of the star rotation before collapse is 1.0e7 s what its period after collapse????

Explanation / Answer

a) The moment of inertia of a sphere rotating about its center is

and its angular momentum is

where the angular velocity

Here R1 = 10^4*R2

b)

c) Rotational kinetic energy is

Since, rotational KE is independant of the radius, it will be unchanged. So the ratio will be 1.

d) The period is given as

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