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

Question

Suppose a star the size of our Sun, but of mass 8.0 times as great, was rotating at a speed of 1.0 revolution every 6 days. If it were to undergo gravitational collapse to a neutron star of radius 5 km, losing three quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times and that the lost mass carries off no angular momentum. If the answer is explained well and is not just copied from a similar question, I will rate lifesaver. I haven't understood any of the similar problems on this site.

Explanation / Answer

use conservation of momentum (the hint is the last statement that no momentum is carried off) this tells you that I w before mass loss = I w after mass loss, where I is the moment of inertia and w the angular velocity the other hint is that the star stays as a sphere, and the moment of inertia of a sphere is 2/5 MR^2 so before mass loss, we have I=1/5 (8M)(7x10^8m)^2 and w = 2 pi/13 days after mass loss, we have I=1/5(2M)1.5x10^4m)^2 and we solve for w(after) we have: 1/5(8M)(7x10^8)^2 (2 pi/13 days) = 1/5(2M)(1.5x10^4m)^2 w (after) solve for w(after), and you will see how conservation of angular momentum allows neutron stars to rotate very rapidly

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