Problem 11.81 Part A Suppose a star the size of our Sun, but with mass 8.0 times
ID: 1790288 • Letter: P
Question
Problem 11.81 Part A 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 8.8 days. If it were to undergo gravitational collapse to a neutron star of radius 14 km , losing of its mass in the process, what would its rotation speed be? Assume the star is a uniform sphere at all times. Assume also that the thrown-off mass carries off no angular momentum. Express your answer using two significant figures. rev/s Submit My Answers Give Up Incorrect; Try Again; 8 attempts remaining Part B Assume also that the thrown-off mass carries off its proportional share of the initial angular momentum. Express your answer using two significant figures. rev/s Submit My Answers Give Up ContinueExplanation / Answer
I = 2 m r^2 / 5
initially, Ii = 2 (8 M ) (R^2) / 5 = 3.2 M R^2
wi = 1 rev / 8.8 days = 1 rev / (8.8 x 24 x 3600)
wi = 1.315 x 10^-6 rev/s
Li = Ii wi = 4.209 x 10^-6 M R^2
(A) If = 2 (8 M / 4) (14/6371 R)^2 / 5 = 3.863 x 10^-6 M R^2
Applying angular momentum conservation,
Li = Lf
4.209 x 10^-6 M R^2 = 3.862 x 10^-6 M R^2 w
w = 1.09 rev/s
(B) L1f = (3/4) (4.209 x 10^-6)
4.209 x 10^-6 M R^2 = (3.862 x 10^-6 M R^2 w ) + (3/4)(4.209 x 10^-6)
w =0.272 rev/s