Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotat
ID: 1262358 • Letter: S
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 8.9 days. If it were to undergo gravitational collapse to a neutron star of radius 15km , losing 34 of its mass in the process, what would its rotation speed be? Assume the star is a uniform sphere at all times.
a) Assume also that the thrown-off mass carries off no angular momentum.
b) Assume also that the thrown-off mass carries off its proportional share (34) of the initial angular momentum.
Explanation / Answer
I1 = (2/5)*8*M*R^2 = 8*2e30*695500000 = 4.4512e+39
M' = (1/4)*8*M
I2 = (2/5)*M'*R'^2 = (2/5)*(1/4)*8*2e30*(15000*15000) = 3.6e+38
from momentum conservation
I1*w1 = I2*w2
4.4512e+39*1/8.9 = 3.6e38*w2
w2 = 1 revolution in 1.389 days
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b) L2 = (1/4)*L1
I2*w2 = (1/4)*I1*w1
3.6e38*w2 = (1/4)*4.4512e+39*1/8.9
w2 = 1 revolution in 0.35 days
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