Neutron stars, or pulsars, spin very quickly about their axes. Their high rate o

Question

Neutron stars, or pulsars, spin very quickly about their axes.
Their high rate of spin is the result of the conservation of
angular momentum during the formation of the neutron star
by the gradual contraction (shrinking) of an initially normal
star.
(a) Suppose that the initial star is similar to the Sun, with a
radius of 7.0 * 10^8 m and a rate of rotation of 1.0 revolution
per month. If this star contracts to a radius of
1.0 * 10^4 m, by what factor does the moment of inertia
increase? Assume that the relative distribution of mass
in the initial and the final stars is roughly the same.
(b) By what factor does the angular velocity increase? What
is the final angular velocity?

Explanation / Answer

I1 = MR^2

I2 = MR'^2

R' = 1 x 10^4 m

M = mass remain same

I2/I1 = (1 x 10^4)^2 / ( 7 x 10^8)^2 = 2.04 x 10^-10

part b )

angular momentum is conserve

I1w1 = I2w2

MR^2 * 1 rev/month = MR'^2*wf

wf = 4.9 x 10^9 rev/month

wf/wi = 4.9 x 10^9

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