Posted by **donut** on Thursday, May 10, 2012 at 12:10am.

A star with an initial radius of 1.0 x 10^8 m and period of 30.0 days collapses suddenly to a radius of 1.0 x 10^4 m. (a) Find the period of rotation after collapse. (b) Find the work done by gravity during the collapse if the mass of the star is 2.0 x 10^30 kg. (c) What is the speed of the person standing on the equator of the collapsed star? (Neglect any relativistic or thermal effects, and assume the star is spherical before and after it collapses.

- physics -
**Elena**, Thursday, May 10, 2012 at 3:57pm
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 = .........

- physics -
**Anonymous**, Saturday, April 26, 2014 at 11:56pm
6.3

## Answer this Question

## Related Questions

- physics - A star with an initial radius of 1.0 x 10^8 m and period of 30.0 days ...
- Another astronomy (algebra-based physics) question - I’d prefer thorough ...
- Physics please help!! - The mass of a star is 1.49·1031 kg and it performs one ...
- Physics - A star with the same mass and diameter as the sun rotates about a ...
- general physics - COMPLETELY STUCK? The period of rotation of the Moon is about ...
- physics - A star the size of the sun has a mass 8 times as great. It rotates on ...
- physics - pulsar is a rapidly rotating neutron star that emits radio pulses ...
- physics?? - Two newly discovered planets follow circular orbits around a star in...
- physics - Astronomers determine masses of distant objects by observing their ...
- physics - Astronomers determine masses of distant objects by observing their ...