# Angular momentum question

ok the question is a spherical star expands to 6 times its volume but its mass remains constant and is uniformly distributed - how does the period of rotation change?

obviously it rotates slower and thus the period goes up, but i dont know how to solve it mathematically. can someone give me some pointers and get me going in the right direction? is there a main equation i should be using and do i need to find the ratio of the radii before and after the star expands?

thanks.

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Doc Al
Mentor
Hint: What's conserved? How does the rotational inertia change when the star expands? (Yes, you'll need to know how the radius changes.)

angular momentum is conserved.

and rotational inertia increases as the star expands, hence the angular velocity will go down to conserve angular momentum (L=Iw), right?

and if the volume goes up by 6 times, it means the radius went up by ~1.8 times.

do i then square that value because I=mr^2?

which means the inertia went up by (1.8)^2 = 3.3 and therefore the angular velocity (w) went down by 3.3 to compensate for that? am i understanding this correctly?

Doc Al
Mentor
Sounds like you have the right idea!

$$I = 2/5 m r^2$$

$$r_2 = 6^{1/3}r_1$$

$$I_2 = 6^{2/3}I_1$$

BobG
Homework Helper
dnt said:
angular momentum is conserved.

and rotational inertia increases as the star expands, hence the angular velocity will go down to conserve angular momentum (L=Iw), right?

and if the volume goes up by 6 times, it means the radius went up by ~1.8 times.

do i then square that value because I=mr^2?

which means the inertia went up by (1.8)^2 = 3.3 and therefore the angular velocity (w) went down by 3.3 to compensate for that? am i understanding this correctly?
Double check your formula for moment of inertia of a solid sphere. You used the basic formula for a point mass or ring. You can derive the formula for a sphere yourself, or look them up: moment of inertia
None the less, the difference in the formulas is a constant, so it doesn't change the proportions. You'll get the same ratio either way.