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 8.3 days. If it were to undergo gravitational collapse to a neutron star of radius 14 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.

Part A

Assume also that the thrown-off mass carries off no angular momentum.

Express your answer using two significant figures. (asnwer is in rev/s)

Part B

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.(answer in rev/s)

Explanation / Answer

Mi = initial mass = 8 x 1.98 x 1030 kg

Ri = initial radius = 6.96 x 108 m

wi = initial angular velocity = 1 (2pi)/(24 x 3600 x 8.3) = 2 x 3.14 /(24 x 3600 x 8.3) = 8.8 x 10-6 s

wf = final angular velocity

Mf = final mass = (0.25) (8 x 1.98 x 1030 )

Rf = final radius = 1.4 x 104 m

using conservation of angular momentum

Ii wi = If wf

(0.4) (Mi Ri2) wi = (0.4) (Mf Rf2) wf

(8 x 1.98 x 1030) (6.96 x 108)2 (8.8 x 10-6) =  (0.25) (8 x 1.98 x 1030 ) (1.4 x 104)2 wf

wf = 8.7 x 104 rad/s

b)

(0.25)Ii wi = If wf

(0.25)(0.4) (Mi Ri2) wi = (0.4) (Mf Rf2) wf

(0.25) (8 x 1.98 x 1030) (6.96 x 108)2 (8.8 x 10-6) =  (0.25) (8 x 1.98 x 1030 ) (1.4 x 104)2 wf

wf = 2.2 x 104 rad/s

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