# Period of the sun

Could someone help me start this problem. My mind it in the angular momentum mode and I am having trouble seeing where to start on this one.

The sun's radius is 6.96E8m and it rotates with a period of 25.3d. Estimate the new period of rotation of the sun if it collapses with no loss of mass to become a neutron star of radius 5.5km. Give the result in seconds.

Thank you very much!

## Answers and Replies

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With the given radius you can find $$I_{initial}$$ and $$I_{final}$$. With the given period, find out $$\omega_{initial}$$. Then you use conservation of angular momentum to achieve your answer.

as such...(you don't need the moments of inertia exactly because it maintains a spherical shape and same mass so those factor out)

$$(r_i)^2 \omega_i = (r_f)^2 \omega_f$$
$$\omega_f = \frac{(r_i)^2 \omega_i}{(r_f)^2}$$
$$T_{new} = \frac{2 \pi}{\omega_f}$$