Angular Momentum Conservation Problem

[akan]

Homework Statement

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 M_sun, 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 M_sun and a rotation period of 131 s.

Homework Equations

M_sun = 1.99 × 10³⁰ kilograms
M₁ = 1.0 M_sun
R₁ = 6.96 * 10⁸
T₁ = 25 days = 2 160 000 seconds

M₂ = 0.62 M_sun
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

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?

 

[hage567]

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

 

[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?

 

[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?

 

[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.