The mass of a star is 1.570 x 10^31 kg and it performs one rotation in 27.70 days. Find its new period (in days) if the diameter suddenly shrinks to 0.550 times its present size. Assume a uniform mass distribution before and after.(adsbygoogle = window.adsbygoogle || []).push({});

I used conservation of momentum

[tex] I \omega_o = I \omega_f [/tex]

I said that the initial diameter was 1 since it wasn't given. This would mean the initial radius was .5.

I found the initial angular velocity by doing [tex] 2 \pi rad / 27.70 day [/tex], divided by 24 hr, and then divided by 60 min, and divided by 60 s to get 2.63 x 10^-6 rad/s.

So [tex] L_o = (1.570 x 10^{31})(.5^2)(2.63x 10^{-6})[/tex] = 1.03 x 10^{25}

The diameter is then shrunk by .550. This means the new radius is .275.

So [tex] L_f= (1.570 x 10^{31})(.275^2) \omega = 1.19 x 10^{30} \omega [/tex]

Solving for omega gave me 8.66 x 10^ {-6} \frac {rad} {s} .

My answer has to be in days, and I'm not really sure how to convert or if I even did this right. Please help!

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# Period of a star / momentum

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