One more Universal Gravitation

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Neutron stars, formed from supernova remnants, can have significant angular speeds due to their density. The discussion revolves around calculating the maximum angular speed for a neutron star with twice the mass of the Sun and a radius of 5.0 km, ensuring that surface matter is held in orbit by gravitational force. The escape velocity at the star's surface is calculated to be approximately 2.2469 x 10^9 m/s. Participants emphasize the relationship between angular speed and linear speed at the equator, noting that gravity acts as the centripetal force needed for rotation. Understanding these concepts is crucial for solving the problem of angular speed in neutron stars.
Antepolleo
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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.
 
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What is the escape velocity at the surface of such a star?
 
Originally posted by StephenPrivitera
What is the escape velocity at the surface of such a star?

That would be

<br /> v_{esc} = \sqrt_{\frac{2GM}{R}}<br />

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.
 
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:
Originally posted by Antepolleo
I will be honest, I'm not even sure where to start... any hints on where to begin would be appreciated.
Consider that the rotating surface is centripetally accelerated and that gravity is the centripetal force.
 
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