Period of Star When Diameter Shrinks

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Homework Help Overview

The problem involves a star with a specified mass and rotation period, exploring how its rotation period changes when its diameter shrinks to a fraction of its original size. The context is within the realm of rotational dynamics and conservation of angular momentum.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the conservation of angular momentum and how to set up the equation correctly. There are questions about unit consistency and the implications of changing the diameter on the period of rotation.

Discussion Status

Some participants are attempting to clarify the relationship between initial and final angular velocities, while others are exploring the correct manipulation of the equations. Guidance has been provided regarding unit conversions and the structure of the equations, but there is still uncertainty regarding the calculations.

Contextual Notes

Participants are navigating the challenge of ensuring unit consistency, particularly when converting between days and seconds, as well as the implications of the problem's requirements for the final answer format.

lew44
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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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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?
 
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.
 
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
 
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
 

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