Angular Velocity of a neutron start

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SUMMARY

The discussion focuses on calculating the maximum angular speed of a neutron star with a mass of 1.991 x 1030 kg (twice the mass of the Sun) and a radius of 13.5 km. The key equation used is the escape velocity formula, Vesc = √(2GM/R), where G is the gravitational constant. The calculated angular speed must ensure that the gravitational force at the equator is sufficient to keep matter in orbit, with the expected range being between 5000 and 20000 radians/sec. The participant expresses uncertainty about the approach but recognizes the need to equate gravitational force with centripetal force.

PREREQUISITES
  • Understanding of gravitational force and centripetal force concepts
  • Familiarity with the escape velocity equation
  • Basic knowledge of neutron star properties
  • Proficiency in unit conversions (e.g., km to meters)
NEXT STEPS
  • Study the derivation of the escape velocity formula in astrophysics
  • Learn about the dynamics of rotating celestial bodies
  • Explore the relationship between mass, radius, and angular velocity in neutron stars
  • Investigate the effects of extreme gravity on matter in neutron stars
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in the mechanics of neutron stars and their rotational dynamics.

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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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Consider a tiny piece of matter at the surface and assume that its acceleration in the radial direction is 0. This means that the gravitational force is equal to...what?
 

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