# Angular Momentum Conservation Problem

1. Sep 9, 2008

### akan

1. The problem statement, all variables and given/known data
When a star like our Sun no longer has any hydrogen or helium "fuel" for thermonuclear reactions in its core, it can collapse and become a white dwarf star. Often the star will "blow off" its outer layers and lose some mass before it collapses into the rapidly spinning, dense white dwarf. Suppose a star with mass 1.0 Msun, with a radius of 6.96×10^8 m and rotating once every 25 days, becomes a white dwarf with a mass of 0.62 Msun and a rotation period of 131 s.

2. Relevant equations
Msun = 1.99 × 1030 kilograms
M1 = 1.0 Msun
R1 = 6.96 * 108
T1 = 25 days = 2 160 000 seconds

M2 = 0.62 Msun
R2 = ?
T2 = 131 seconds

T = 2 pi r / v
= 2 pi r / w r
= 2 pi / w
.:. w = 2 pi / T

I = (2/5)MR2

3. The attempt at a solution
I1 x w1 = I2 x w2
(2/5)(M1 x R12)(2 pi / T1) = (2/5)(M2 x R22)(2 pi / T2)
(M1 x R12)(1 / T1) = (M2 x R22)(1 / T2)
(M1 / M2)(T2 / T1)(R12) = R22
sqrt((M1 / M2)(T2 / T1)(R12)) = R22
R2 = sqrt((1.99*1030)/[(0.62)(1.99*1030)](131/2160000)(6.96*108)2
= 6.88*106 m

Checking the result by plugging into equations shows that I am roughly correct. But Mastering Psychics says I am wrong. Where is the mistake?

2. Sep 10, 2008

### hage567

I get a different answer using your last equation. Perhaps you typed it into your calculator incorrectly?

3. Sep 10, 2008

### akan

Well, I tried typing it a few more times and I am still getting the same answer. I also tried to use the masteringphysics integrated calculator, which is more graphical, but got the same answer. What answer do you get? And are there any errors in any of my formulas?

4. Sep 10, 2008

### hage567

Hmmm, I think I might have typed it into my calculator wrong since I now get the same answer as you. As far as I can tell, your solution is correct. Perhaps check with your teacher to see if the answer given is wrong?

5. Sep 14, 2008

### Jar9284

I have the similar problem as you are except my mass is .6 M$$_{sun}$$ now when pluggin mine in I get the following equation:

R$$_{2}$$ = $$\sqrt{\frac{1.99x10^{30}}{(.60 * 1.99x10^{30})} * \frac{131}{2160000} * 6.96x10^{8}}$$ = 70351.8 = 70000 if you do 2 sig figs, but according to mastering physics is wrong so any help on where its going wrong would suffice.