Angular Velocity of a neutron start

AI Thread Summary
To determine the greatest possible angular speed of a neutron star with twice the mass of the sun and a radius of 13.5 km, the gravitational force must equal the centripetal force acting on the surface matter. The escape speed equation, Vesc = sqrt(2GM/R), is initially used to calculate the escape velocity, but the approach may not directly address the problem of angular velocity. The discussion highlights uncertainty about the correct method to relate gravitational force to the required centripetal acceleration for surface matter. The expected angular speed is suggested to fall within the range of 5000 to 20000 radians/sec. Understanding the balance of forces is crucial for solving the problem accurately.
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Homework Statement



Supposed that the mass of certain spherical neutron star is twice the mass of the sun (1.991*10^30) and its radius is 13.5 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?
The answer is in the range of 5000-20000 radians/sec

Homework Equations



Vesc=sqrt^(2GM/R)

The Attempt at a Solution



I used the escape speed equation. I plugged in the mass of the star times G, divided by the radius of the star (13.5km or 13500 m) and then solved for Vesc. But I'm not really sure that's what I am really looking for. I think I might be approaching the problem wrong, but I'm not sure where to go from here.
 
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