Period of Star When Diameter Shrinks

[lew44]

Homework Statement

The mass of a star is 1.370×1031 kg and it performs one rotation in 38.10 day. Find its new period (in days) if the diameter suddenly shrinks to 0.330 times its present size. Assume a uniform mass distribution before and after.

Homework Equations

Ii * Wi = If * Wf
2/5MR^2 * 1rot/38.1 days = (2/5MR^2*0.330^2) * Wf

The Attempt at a Solution

I am not sure what cancels out

I thought it would be something like

1rot/38.1days = .330^2 * Wf

solve for Wf

But that didn't work. .241s was not correct

 

[ehild]

Take care of the units. rot/day is not second.

ehild

 

[lew44]

I still don't understand because if I change the bottom number to seconds I still have rot/sec and that is not seconds. Plus it asks for the period in days so doesn't that factor in?

 

[ehild]

wi and wf have the same units.

ehild

 

[lew44]

it asks for the new period in days! I am not sure what to do with this problem

 

[lew44]

I am getting like 2198.249 as an answer.

 

[ehild]

You replaced wi by 1rot/39.1days. Then you should do the same with wf: wf=1rot/xdays.

Rewrite your equation

1rot/38.1days = .330^2 * Wf

as

1rot/38.1days = 0.330^2* (1rot/x days)--->1/38.1 =0.330^2/x.

Solve for x.

ehild

 

[lew44]

thank you, i think i just didn't understand that you needed the x on the other side of the equation and that is what was giving me such a large answer