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)

jamesj · Answer

What is the angular momentum of a sphere rotating about its own axis?

jamesj · Answer

In general, angular momentum L is the product of the moment of inertia and angular velocity:
$$ L = I \omega $$
Clearly in this scenario $ I $ changes but L is conserved.  In other words:
$$ I_1 \omega_1 = I_2 \omega_2 $$
You need to solve for $ \omega_2 $.