Suppose a star the size of our Sun, but of mass 9.0 times as great, were rotating at a speed of 1.0 revolution every 17 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

Use the conservation of angular momentum; angular momentum at the beginning = angular momentum at the end

Conservation of angular momentum:

I1 w1 = I2 w2

Where I is the moment of inertia. For a sphere, I=2/5 m R^2. Substituting into the equation above we get

w2 = I1 w1 / I2 = w1 m1 R1^2 / (m2 R2^2)

w2 = w1 4 * (R1/R2) ^2

= 4 * (1) * (7E5/7.5) ^2

= 3.48E10 revs / (17days)

= 2.04705882 x 10^9 revs/sec