3. Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 1014 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star’s initial radius was 7.0 x 105 km (comparable to our sun); its final radius is 16 km. If the original star rotated once in 30 days, find the angular speed of the neutron star. (Assume no mass was lost in the collapse)

Question

3.	Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 1014 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star’s initial radius was 7.0 x 105 km (comparable to our sun); its final radius is 16 km. If the original star rotated once in 30 days, find the angular speed of the neutron star. (Assume no mass was lost in the collapse)

anonymous · Answer

correct, with no mass loss, the ratio of radii^3 gives 1.2 x10^14 as a density factor. 

The question requires conservation of angular momentum, L. 
For a sphere, $$L = \frac{ 2 }{ 5 }m R ^{2}\frac{ 2\pi }{ T }$$ (T is the period or rotation)
You need to just equate the equation using the large radius to the equation using the small radius. This will cancel the mass that you don't know. On the large radius side, you have T (but you will need to put it into seconds), so you will be able to solve for the only unknown, T, on the small radius side giving you the new T.