Question

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 9.0×105 km (comparable to our sun); its final radius is 15 km .

Part A If the original star rotated once in 25 days, find the angular speed of the neutron star. Express your answer using two significant figures.

Answer 1

Let us find out the initial angular speed off the star.

It rotated once in 25 days, so angular velocity is

Now, angular momentum of the system must be conserved.

Modelling the star as a sphere of mass M and initial and final radius as R1 and R2 we must have

is the final angular velocity

Putting the values,

This is the angular speed of the star.