Under some circumstances, a star can collapse into an extremely dense object mad

Question

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 1014 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was 9.0×105 km (comparable to our sun); its final radius is 18 km .

Part A

If the original star rotated once in 27 days, find the angular speed of the neutron star.

Express your answer using two significant figures.

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Explanation / Answer

According to the given problem,

Conserve angular momentum: initial I = final I
For a solid sphere, I = (2/5)mr²
initial = 2 rads / T = 2 / (27days * 24hr/day * 3600s/hr) = 2.7*10-6 rad/s
(2/5)*m*(9*105 km)² * 2.7*10-6rad/s = (2/5)*m*(18 km)² *
(2/5)m cancels;
= 6.7*103 rad/s

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