Calculate New Period of Star After Shrinking Diameter

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To calculate the new rotation period of a star after its diameter shrinks, the conservation of angular momentum must be applied. The initial angular momentum can be expressed as the product of the star's mass, its initial radius, and its initial rotation period. When the diameter decreases to 0.610 times its original size, the radius also decreases proportionally, affecting the moment of inertia. The new period can be determined by equating the initial and final angular momentum, leading to the formula that incorporates the new radius. This approach allows for the calculation of the star's new rotation period in days.
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The mass of a star is 1.170×1031 kg and it performs one rotation in 28.30 day. Find its new period (in days) if the diameter suddenly shrinks to 0.610 times its present size. Assume a uniform mass distribution before and after.

How do I even start this problem? Can anyone give me step by step how to do this?
 
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Hi joeypeter! :smile:

We can give you one step:

Use conservation of angular momentum (what is it in this case?)
 

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