Determining New Angular Velocity

AI Thread Summary
To determine the new angular velocity of the star after it becomes a white dwarf, the conservation of angular momentum is crucial since there are no external torques acting on the system. The initial moment of inertia (I) of the star is calculated using the formula I=(2/5)MR², resulting in 6.94x10^47 kg·m². After shedding half its mass and contracting, the new radius of the white dwarf is 9.5x10^7 m, which will affect its moment of inertia and angular velocity. The relationship between initial and final angular momentum must be established to find the new angular velocity. Understanding these principles will guide the solution without needing a direct answer.
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Homework Statement


A star with mass 2.4x1030 kg and diameter 1.7x109 m rotates once every 34 Earth days. It eventually dies and becomes a white dwarf, shedding about half of its mass and contracting to a diameter of 1.9x108 m. If we approximate the star as a perfect sphere, what is its resulting angular velocity?

Initial star r = 8.5x108 m
Initial star m = 2.4x1030 kg
Initial star ω = 1 rev/34 days = 1.85x107 rad/s
White dwarf r = 9.5x107 m

Homework Equations


I=(2/5)MR2

The Attempt at a Solution


I'm getting really stuck on this one. I can determine I for the initial star (I=(2/5)(2.4x1030 kg)(8.5x108)2 m=6.94x1047 kgxm2, but from there I'm not sure where to go. I'm not even sure if that's relevant. I'm not looking for a handout here, but any guidance would be appreciated!
 
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Why do you need to know I?
 
There are no external torques in this problem, therefore angular momentum is conserved.

h = Iω
 
Yes, so can you write an equation that shows this?
 
sun18 said:
There are no external torques in this problem, therefore angular momentum is conserved.

h = Iω
Yes, but be careful. What do you think the angular momentum of the shed mass will be at the end?
 

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