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Under some circumstances, a star can collapse into an extremely dense object mad

ID: 1450259 • Letter: U

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

Let M is the mass of neutron star.

R1 = 9.5*10^5 km

R2 = 17 km

T1 = 31 days

T2 = ?

let w1 and w2 are the initial and final angular speeds.

Apply conservation of angular momentum.

I1*w1 = I2*w2

(2/5)M*R1^2*w1 = (2/5)*M*R2^2*w2

R1^2*w1 = R2^2*w2

R1^2*2*pi/T1 = R2^2*2*pi/T2

==> T2 = T1*(R2/R1)^2

= 31*(17/(9*10^5))

= 5.86*10^-4 days

= 5.86*10^-4*(24*60*60)

= 50.6 s