# Conservation of Angular Momentum sun problem

1. Apr 15, 2013

### Godcanthelp

1. The problem statement, all variables and given/known data
When a star like our Sun exhausts its fuel, thermonuclear reactions in its core cease, and it collapses to become a white dwarf. Often the star will blow off its outer layers and lose some mass before it collapses. Suppose a star with the Sun’s mass and radius (the radius of the Sun is 6.96×108m ) is rotating with period 25 days and then it collapses to a white dwarf with 53% of the Sun’s mass and a rotation period of 131 s.

2. Relevant equations
Conservation of Angular Momentum:
Angular Momentuminitial = Angular Momentum final
Angular Momentum = Rotational Inertia (sphere) * Angular Velocity (ω)
Rotational Inertia (sphere) = 2/5MR2

3. The attempt at a solution

Isunsun = Iwdwd
(2/5)*Msun*Rsun2*2∏/(25*24*60*60) = (2/5)*Mwd*Rwd2*2∏/131

Msun*(6.96*108)2*1/(25*24*60*60) = 0.53*Msun*Rwd2*1/131

(6.96*108)2*1/(25*24*60*60) = 0.53*Rwd2*1/131

Rwd2 = 131*(6.96*108)2*1/(25*24*60*60) *1/0.53

Rwd = 7.44526*106m

Which is incorrect.

2. Apr 15, 2013

### collinsmark

Hello Godcanthelp,

Welcome to Physics Forums!

You seem to have left out the the primary goal in the problem statement. Are you supposed to find the white dwarf's radius?

The approach you are using makes a few approximations, such as the original star having a uniform density. And crazy as it sounds, it's difficult to gauge a real star's rotation rate since it rotates at a different angular speed at its equator than it does at it's poles (I know, weird huh).

But let's just approximate it as a rotating, solid sphere with uniform density anyway.

Only 53% of the original star's mass ends up collapsing into a white dwarf. The rest gets blown off.

My guess is you should not start with the angular momentum of the entire star. Instead, only consider the inner 53% of that star. So first, find the radius of the inner 53% by mass of that star. Then apply conservation of angular momentum after that.

Last edited: Apr 15, 2013