A star with the same mass and diameter as the sun rotates about a central axis w

Question

A star with the same mass and diameter as the sun rotates about a central axis with a period of about 26.2 days. Suppose that the sun runs out of nuclear fuel and collapses to form a white dwarf star with a diameter equal to that of the earth. Assume the star acts like a solid sphere and that there is no loss of mass in the process. Radius of the Sun = 9.96x10^8 Radius of the Earth = 6.37x10^6 (a) What would be the new rotation period (s) of the star? (b) What is the ratio of final to initial kinetic energies (Kf=Ki)? I'm pretty sure I did (a) correctly. The answer I got for (a) is 189.6 seconds I don't know how to calculate the KE of the masses

Explanation / Answer

applying conservation of momentum we fet

I1w1=I2w2

thus r1^2/T1=r2^2/T2

T2=R2^2/R1^2*T1

(6.37x10^6)^2*/[9.96x10^8]^226.2day=189.6 second

b>.ratio of Ke=R2^2*T1^2/R1^2*T2^2=5.97*10^6

thus ke ratio is given by 1/2Iw^2..

where

I= moment of inertia which will be 2/3mr^2 in case of sphere..

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