Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotat

Question

Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 8.7 days. If it were to undergo gravitational collapse to a neutron star of radius 15 km , losing 34 of its mass in the process, what would its rotation speed be? Assume the star is a uniform sphere at all times.Assume also that the thrown-off mass carries off no angular momentum.Assume also that the thrown-off mass carries off its proportional share (34) of the initial angular momentum.

Explanation / Answer

M1= M

M2 = M- 3M/4 = M/4

R1 = 695700 km

R2 = 15 km

W1 = 1/ 8.7 = 0.1149 rev/day

from conservation of angular momentum

I1 W1 = I2 W2

2/5 M R1^2 W1 = 2/5 M/4 R2^2 W2

M (695700)^2*0.1149=M/4 *15^2* W2

W2 = 9.89 X 10^8 rev/day

w2 = 1.145 x 10^4 rev/sec

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