Conservation of Angular Momentum sun problem

[Godcanthelp]

Homework Statement

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.

Homework Equations

Conservation of Angular Momentum:
Angular Momentum_initial = Angular Momentum _final
Angular Momentum = Rotational Inertia (sphere) * Angular Velocity (ω)
Rotational Inertia (sphere) = 2/5MR²

The Attempt at a Solution

ω_sun = 2∏/(25*24*60*60) rad/sec
ω_wd = 2∏/131 rad/sec

I_sun*ω_sun = I_wd*ω_wd
(2/5)*M_sun*R_sun²*2∏/(25*24*60*60) = (2/5)*M_wd*R_wd²*2∏/131

M_sun*(6.96*10⁸)²*1/(25*24*60*60) = 0.53*M_sun*R_wd²*1/131

(6.96*10⁸)²*1/(25*24*60*60) = 0.53*R_wd²*1/131

R_wd² = 131*(6.96*10⁸)²*1/(25*24*60*60) *1/0.53

R_wd = 7.44526*10⁶m

Which is incorrect.

 

[collinsmark]

Hello Godcanthelp,

Welcome to Physics Forums!

Homework Statement

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.

Homework Equations

Conservation of Angular Momentum:
Angular Momentum_initial = Angular Momentum _final
Angular Momentum = Rotational Inertia (sphere) * Angular Velocity (ω)
Rotational Inertia (sphere) = 2/5MR²

The Attempt at a Solution

ω_sun = 2∏/(25*24*60*60) rad/sec
ω_wd = 2∏/131 rad/sec

I_sun*ω_sun = I_wd*ω_wd
(2/5)*M_sun*R_sun²*2∏/(25*24*60*60) = (2/5)*M_wd*R_wd²*2∏/131

M_sun*(6.96*10⁸)²*1/(25*24*60*60) = 0.53*M_sun*R_wd²*1/131

(6.96*10⁸)²*1/(25*24*60*60) = 0.53*R_wd²*1/131

R_wd² = 131*(6.96*10⁸)²*1/(25*24*60*60) *1/0.53

R_wd = 7.44526*10⁶m

Which is incorrect.

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.