How Does the Rotation Period Change When a Star Expands to Six Times Its Volume?

[dnt]

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 don't 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.

 

[Doc Al]

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

 

[dnt]

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]

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]

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.