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 31 days, find the angular speed of the neutron star.

Explanation / Answer

given that

initial radius Ri = 9*10^5 km = 9*10^8 m

final radius = Rf = 17 km = 17000 m

T = 31 days =31day*86400s/day = 2678400 s

conserve angular momentum
If*wf = Ii*wi

wi = angular speed before collapse .

wf = angular speed after collapse.

If= inertia after collapse

Ii = inetia before collapse

wi = 2*pi / T

wi = 2*3.14 / 2678400

wi = 0.0000023

so

If*wf = Ii*wi

2/5*m*Rf^2 *wf = 2/5*m*Ri^2*wi

wf = Ri^2*wi / Rf^2

wf = (9*10^8)^2 * 0.0000023 / (17000)^2

wf = 6.4*10^(-7)*10^16 / 10^6

wf = 6400 rad/s

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