Physics Problem: Angular speed ...?

Question

Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose that the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed it can have so that the matter at the surface of the star on its equator is just held in orbit by the gravitational force.

I don’t understand this problem in my book. Please help me by explaining how to solve and what equations used to solve them. Thank You.

Answer 1

You have to calculate what the acceleration is due to gravity at 10 km radius for the mass = 2 solar masses  with  a radius 10 km.

Then you have to equate this acceleration to that of the centripetal acceleration you would have if this mass were spinning at a angular speed that would give you a centripetal acceleration equal to the calculated gravitational acceleration. Any faster angular speed would eject the mass.

You should get

w = sqrt(2GMs/R^3)

Where

w= angular speed in radians per second

Ms = Mass of the sun

R = 10,000 m

G = Universal Gravitational Constant