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 10 km, losing | 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) the initial angular momentum. Express your answer using two significant figures.

Explanation / Answer

Using law of conservation of angular momentum

then

Li = Lf

I1*w1 = I2*w2

moment of inertia of solid sphere is (2/5)*M*R^2

then

R is the radius of the sun = 695700 km = 6.95*10^8 m

w1 = 2*pi/T1 = (2*3.142)/(8.9*24*60*60)

((2/5)*M*R^2)*((2*3.142)/(8.9*24*60*60))= (2/5)*(1/4)*M*(10*10^3)^2*w2

(6.95*10^8)^2*((2*3.142)/(8.9*24*60*60))= ((10^8)*w2)/4

w2 = 1.58*10^5 rad/sec = 2.52*20^4 rev/sec

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Part B)

Li = (1/4)*Lf

((2/5)*M*R^2)*((2*3.142)/(8.9*24*60*60))= (1/4)(2/5)*(1/4)*M*(10*10^3)^2*w2

(6.95*10^8)^2*((2*3.142)/(8.9*24*60*60))= ((10^8)*w2)*0.25/4

w2 = 6.32*10^5 rad/sec = 1*10^5 rev/sec

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