Conservation of Angular Momentum of Star

AI Thread Summary
To find the new angular velocity of a star after its diameter shrinks to 0.49 times its original size, the conservation of angular momentum principle is applied. The initial angular momentum is calculated using the formula L = Iw, where I is the moment of inertia for a solid sphere. The moment of inertia for the final state must account for the reduced radius, which is squared in the calculations. The user is reminded that the radius will cancel out when setting the initial and final angular momentum equal, simplifying the problem. Proper attention to the squaring of the 0.49 factor is crucial for an accurate solution.
ganondorf29
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Homework Statement


The mass of a star is 1.51·1031 kg and its angular velocity is 1.50E-7 rad/s. Find its new angular velocity if the diameter suddenly shrinks to 0.49 times its present size. Assume a uniform mass distribution before and after. Icm for a solid sphere of uniform density is 2/5 mr2


Homework Equations



L=Iw

L(int)=L(final)


The Attempt at a Solution



L(int) = [(2/5)M*R^2]*(wint)
L(final) = [(2/5)M*(0.49)*R^2]*(wfinal)

And I got stuck there. I don't know how to find the radius and I think that's holding me back.
 
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Note that it will cancel out when you set them equal since you've expressed the final radius in terms of the initial radius.

Be careful with the 0.49, it should be squared as well.
 

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