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 15 km .

Part A

If the original star rotated once in 35 days, find the angular speed of the neutron star.

Explanation / Answer

From conservation of angular momentum

initial Iw = final Iw

I = (2/5) * m * r2

w = 2 pi / T = 2 pi / (35 days* 24 hr/day * 3600 s/hr) = 2.08 * 10-6 rad/s

2/5 * m * (9 * 105 * 103)2 * 2.08 * 10-6 = 2/5 * m * (15 * 103)2 * w

w = 2.08 * 10-6 * [9 * 105 / 15]2

angular speed w = 7488 rad/s

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