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 7.0×105 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.

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 7.0×105 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

conserve angular momentum
iw = IW
let capitals be the initial values before the collapse and the normal letters be the final values after collapse
where
w = angular speed, i = inertia, m = mass, r = radius,
and
T = 31day * 86400s/day = 2678400s is the initial period
for a sphere the inertia, i = 2mr²/5 so
iw = IW
gives
2mr²w/5 = 2mR²W/5
r²w = R²W

gives w = R²W/r²
then note that W = 2/T
so
w = R²(2/T) /r² = 2R² /Tr² 2 * 3.14 *(7.0 x 10^5)^2 Km^2/ 2678400 * (17 )^2 Km^2 = 3975.41rad/s

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