# One more Universal Gravitation

1. Dec 11, 2003

### Antepolleo

Ok, here's the problem:

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 5.0 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 will be honest, I'm not even sure where to start... any hints on where to begin would be appreciated.

2. Dec 11, 2003

### StephenPrivitera

What is the escape velocity at the surface of such a star?

3. Dec 11, 2003

### Antepolleo

That would be

$$v_{esc} = \sqrt_{\frac{2GM}{R}}$$

which I believe is about 2.2469 x 109.

How would I relate this to the answer? I'm afraid I can't see the connection.

4. Dec 12, 2003

### StephenPrivitera

I'll take you through it.
How is angular speed of the star related to the linear speed of an object on the equator of the star?

Last edited: Dec 12, 2003
5. Dec 12, 2003

### Staff: Mentor

Consider that the rotating surface is centripetally accelerated and that gravity is the centripetal force.