- #1

Vitani11

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## Homework Statement

The sun is a pretty typical star with a mass of 1.99x10

^{30}kg and a radius of 6.69x10

^{8}m. Since it isn't solid, it doesn't rotate uniformly, but has an average rotation rate of 1rev/25d. A star with a mass about about three times that of the Sun eventually explodes as a supernova and leaves behind its collapsed remnants - a neutron star or a black hole. Neutron stars masses are somewhat lower than the masses of the original stars, but have much smaller radii, less than 10 km. Newly-collapsed neutron stars emit beams of radio waves; since they rotate so quickly, the beams may intersect Earth at regular intervals. To produce the observed pulsar rates, the rotation rates must vary from 1rev/s to 1000rev/s.

What would be the approximate rotation rate of the Sun if it became a neutron star with a radius of 10km? Assume it is spherical, with a uniform mass distribution, and that its moment of inertia if 0.059MR

^{2}(Since it is not a solid you can not use I for a solid sphere).

## Homework Equations

I

_{1}ω

_{o}=I

_{2}ω

_{f}conservation of angular momentum

ω

_{avg}= 1rev/25d

ω

_{0}= 1rev/(25x2x6.69x10

^{8}m) = 2.99x10

^{-11}rev/s

I

_{1}=0.059(1.99x10

^{30}kg)(6.69x10

^{8}m)

^{2}

I

_{2}= 0.059(1.99x10

^{30})(10m)

^{2}

ω

_{f}= ?

## The Attempt at a Solution

[/B]

I used I

_{1}ω

_{o}=I

_{2}ω

_{f}and solved for ω

_{f}. After I solved for this I got 133,800rev. I then divided this final answer by 25d, or 25x2x10km since the suns radius is now that of a neutron star instead of it's original 6.69x10

^{8}m. This gave me a value of 267.7 rev/s, which according to the problem statement makes sense. I'm not exactly confident in my method though so I would like to know if this is correct.

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