How Does a Star's Diameter Change with Its Rotation Period?

[nnokwoodeye]

Homework Statement

A star of mass 1.81×1031 kg and diameter 8.10E+9 m rotates with a period of 25.0 days. Suddenly the star changes size, and rotates with a new period of 18.0 days. Assuming a uniform density both before and after the size change, what is the new diameter of the star?

Homework Equations

Volume = 4/3*3.14*R^3
Density = M / VOL
I =2/5*M*R^2

The Attempt at a Solution

R(initial) = 8.10*10^9/2=4.05*0^9
Volume(initial) = 4/3*3.14*(4.05*10^9)^3=2.782*10^29
Density= (1.81*10^31/(2.782*10^29)=65.061
I(initial)=2/5*(1.81*10^31)*(4.05*10^9)^2=1.187*10^50
I(final)=2/5*65.061*4/3*3.14*Rf^3*Rf^2=109.01Rf^5
I(initial)*W(initial)=I(final)*W(final)
1.187*10^50*(2*3.14/25)=109.01*(2*3.14/18)*R(final)^5
R(final)^5=1.187*10^50*(2*3.14/25)/(109.01*[2*3.14/18])
R=(2.983*10^49/38.051)*10^(-5)=3.792*10^9
K=2R=7.58*10^9

the computer said that this answer is wrong and i don't know why

 

[ideasrule]

I(final)=2/5*65.061*4/3*3.14*Rf^3*Rf^2=109.01Rf^5

109.01 is not right. Try recalculating that number.

 

[kerimek]

Thank you for sharing your attempt at solving this problem. It seems like you have used the correct equations and have followed the right steps in your solution. However, there may be a mistake in your calculations or in converting units. I would suggest double-checking your calculations and units to see if you can identify where the error may be. It may also be helpful to break down the problem into smaller steps and solve for each step separately to ensure accuracy. Additionally, it may be helpful to consult with a peer or your instructor for assistance. Keep up the good work and don't get discouraged, sometimes solving complex problems can be challenging but with persistence and attention to detail, you can find the correct solution.