How Fast Can Neutron Stars Spin Before Losing Surface Material?

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Neutron stars, formed from supernova remnants, can rotate rapidly due to their extreme density. To determine the maximum angular speed before losing surface material, one must equate gravitational force to centrifugal force at the equator. While some suggest calculating escape velocity first, others argue it's unnecessary for this problem. The key is understanding that at the equator, the gravitational force must balance the centrifugal force for matter to remain on the surface. The discussion highlights differing approaches to solving the problem, emphasizing the importance of force balance.
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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.

First I would find escape velocity
https://www.physicsforums.com/latex_images/11/112728-0.png
And using that velocity as the tangent I could find the angular velocity? Is that a correct assumption?
 
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Hmm, this problem is a little tricky in disguise. If matter at the equator is JUST held on my gravity, that means the object is ALMOST weightless. Use a force balance and set that equal to m*centripedal acceleration and then ask yourself what it means to be weightless. Where does that get you?
 
I think you have my question confused with that of the person below me !
 
That's interesting. I think you have your question confused with another one! No, but really...you can do your problem either way. It's just easier the way I said in my opinion.
 
kim3648 said:
First I would find escape velocity
https://www.physicsforums.com/latex_images/11/112728-0.png
And using that velocity as the tangent I could find the angular velocity? Is that a correct assumption?

It's not necessary here to find escape velo. The force due to gravity should be equal to the centrifugal force at the equator. The same as dwintz02 said.
 
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dwintz02 said:
That's interesting. I think you have your question confused with another one! No, but really...you can do your problem either way. It's just easier the way I said in my opinion.

He can't do it using escape velocity.
 
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TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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