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 8.9 days. If it were to undergo gravitational collapse to a neutron star of radius 15 km losing 3/4 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. Express your answer using two significant figures. Assume also that the thrown-off mass carries off its proportional share (3/4) of the initial angular momentum. Express your answer using two significant figures.

Explanation / Answer

There are 768960 seconds 8.9 days...
so the initial angular velocity is 1 / 768960 = 1.3 x 10^(-6) rev/s

Angular Momentum = I
= Angular Velocity
I = Moment of Inertia of a Sphere = 2/5mr²

L = 2/5mr²

Assuming angular momentum is conserved...

2/5(m1)(r1)²(1) = 2/5(m2)(r2)²(2)

(m1)(r1)²(1) = (m2)(r2)²(2)

m1 = 8 suns
m2 = 2 suns
r1 = 0.7 x 10^6 km ...radius of the sun
r2 = 15 km
1 = 1.3 x 10^(-6) rev/s

(8)(0.7 x 10^(6))²(1.3 x 10^(-6)) = (2)(15)²(2)

2 = 11324.44 rev/s

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