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

Question

Suppose a star the size of our Sun, but of mass 8.0 times as great,were rotating at a speed of 1.0 revolution every 11 days. If it were to undergo gravitational collapseto a neutron star of radius 13 km, losing3/4 of its mass in the process, what would its rotation speed be?Assume the star is a uniform sphere at all times. (a) Assume that the thrown-off mass carries offno angular momentum,
1 rev/s

(b) Assume that the thrown-off mass carries off its proportionalshare (3/4) of the initial angular momentum.
2 rev/s (a) Assume that the thrown-off mass carries offno angular momentum,
1 rev/s

(b) Assume that the thrown-off mass carries off its proportionalshare (3/4) of the initial angular momentum.
2 rev/s

Explanation / Answer

if the intial anular mometum of the rotating star(sphere shape ) = I I = moment of inertia of the sphere = 2Mr^2 /5 r = raidus of the star = radisu of sun M = mass of the star = angularvelocity of the star = 2/T T = time period for 1 rotation = 11*24*3600sec final mass of the star after becomming neutron starM' = 3M /4. I' = 2M'r'^2/5 r' =13000 m angular velocity = ' = 2 /T '. final angular mometum = I'' conservation of angular meometum demands                       I =I'' from the given values , using relations given above wecan sovle for angular velocity of neutron star '   

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