Posted by donut on Thursday, May 10, 2012 at 12:10am.
R = 1•10^8 m, r =1•10^4 m, m = 2•10^30 kg. T1 = 30 days
Since there are no mass loss and no external torques, the angular moment of the star is conserved.
I1•ω1 = I2•ω2.
ω=2•π/T
I1•2•π/T1 = I2•2•π/T2.
For uniform sphere of constant mass I1= 2•m•R²/5, I2 = 2•m•r²/5,
2•m•R²•2•π /5 •T1 = 2•m•r²•2•π /5 • T2.
R² /T1 = r² /T2.
T2 =(r/R)² •T1 = (1•10^4/10^8)² •30 = 30•10^-8 days =0.026 s.
(b) W = KE1 –KE2 = I1• ω1²/2 – I2• ω2²/2 = I1•4•π²/2•T1² - I2•4•π²/2•T2² =
= (2•m•R²/5) •(4•π²/2•T1²) - (2•m•r²/5) •(4•π²/2•T2²) =
= (4•m•π²/5) •{(R/T1)² -( r/T2)²} = .............
(c) v =ω2•r = 2•π•r/T2 = .........
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