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 17 km .

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

Explanation / Answer

mass will not change

moment of inertia I = m*r^2

so Ii = m*(9000*10^5)^2 , If = m*(17000)^2

according to angular momentum conservation

Li = Lf

=> Ii*Wi = If*Wf

=> Wf = Wi*(Ii/If) = (81*10^16/2.89*10^8)*(1/27) = 28.027*10^8 revolutions/day

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