Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotat

Question

Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 8.3 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km , losing 34 of its mass in the process, what would its rotation speed be? Assume the star is a uniform sphere at all times.

Part A

Assume also that the thrown-off mass carries off no angular momentum.

Express your answer using two significant figures.

Part B

Assume also that the thrown-off mass carries off its proportional share (34) of the initial angular momentum.

Express your answer using two significant figures.

Explanation / Answer

we can use conservation of angular momentum,

Iw( initial ) = mr^2 ( 2pi/T)

m= 8 (1.989 × 10^30 )

R= 6.96 x 10^8 ( radius of sun)

w = (2pi / 8.3 x 24 x 3600)= 2.422 x 10^ -4 rad /sec

Initial L = 8 (1.989 × 10^30 ) ( 6.96 x 10^8)^2 ( 2.422 x 10^ -4) = 1866.884 x 10^ 42 kg m/s

Iw (final) = (1/4M) (11x 10^3) ^2 (W)

(M ) (  6.96 x 10^8 )^2 (2pi /  8.3 x 24 x 3600) = (1/4M) (11x 10^3) ^2 (W)

(48.44x 10^16 ) ( 2pi/717120 ) = 0.25 ( 121 x 10^6) W

w=1.402 x 10^5 rad/sec

b) L = 3/4L (thrown away) + 1/4 L (remaining)

1/4 L = 1866.884 x 10^ 42 kg m/s/ 4= 466.721 x 10^ 42 kg m/s

466.721 x 10^ 42 =( 8 (1.989 × 10^30 ) / 4 ( 11x 10^3)^2 w

466.721 x 10^42 / ( 481.338 x 10^ 36) = w

w= 9.69 x 10^ 5 rad /sec

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