# Period of a star

## 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

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

ehild

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
Homework Helper
wi and wf have the same units.

ehild

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

I am getting like 2198.249 as an answer.

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

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

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