Calculating New Period of a Shrinking Star with Uniform Mass Distribution

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Homework Help Overview

The discussion revolves around calculating the new period of a star after its diameter shrinks, while assuming uniform mass distribution. The original poster presents the problem involving the mass of the star and its initial rotation period, seeking guidance on how to approach the calculation of the new period following the change in size.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conservation of angular momentum as a key principle, questioning how to apply it to the problem. There are attempts to express the moment of inertia and angular velocity, with some participants exploring the relationship between initial and final states of the star. Questions arise about the necessary conversions and the implications of changing the radius.

Discussion Status

The discussion is active, with participants providing insights into the equations relevant to the problem. Some guidance has been offered regarding the cancellation of terms and the interpretation of rotational units. However, there is still uncertainty about specific calculations and the application of the moment of inertia formula.

Contextual Notes

Participants note that the problem involves a sudden change in diameter, which is quantified as 0.590 times the original size. There is an emphasis on the uniform mass distribution before and after the change, and the need to consider how this affects the moment of inertia.

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Period of a Star...Please help!

Homework Statement


The mass of a star is 1.250×1031 kg and it performs one rotation in 36.30 day. Find its new period (in days) if the diameter suddenly shrinks to 0.590 times its present size. Assume a uniform mass distribution before and after.

I don't know where to begin!
 
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Think about conservation of angular momentum. What do you know about that?
 
Torque(net) * Change in T = Change in L
Ii * Wi = If * Wf
 
Ii * Wi = If * Wf

OK, so what do you think you might do next? What is I for a solid sphere?
 
2/5MR^2 but how do we get R?
1 rotation/36.3days * pi = W
 
You don't need to know the radius. In the question, you are given the final radius in terms of the first, so it will cancel out.

1 rotation/36.3days * pi = W

Be careful. This isn't quite right. If you are going to convert this, remember there are 2*pi radians in one revolution.
 
Right that's what I thought, but I don't know how to convert rotations to revolutions...
 
1 rotation = 1 revolution. They mean the same thing. There are 2*pi radians per rotation (or revolution).
 
You could leave Wi in terms of rotation/day for this particular problem since all of your other units will cancel out. Of course, if you're unsure how to do it, it's good practice to give it a try.
 
  • #10
Ii * Wi = If * Wf
2/5MR^2 * 1rot/36.3 days = If * Wf
I am not sure how we figure out If?
 
  • #11
If will be the same equation where the only thing that changes is R since the star becomes smaller in diameter. You are given information in the question that allows you to determine how much smaller it becomes

Find its new period (in days) if the diameter suddenly shrinks to 0.590 times its present size.
 
  • #12
Ii * Wi = If * Wf
2/5MR^2 * 1rot/36.3 days = (2/5MR^2*0.590) * Wf
 
  • #13
BuBbLeS01 said:
Ii * Wi = If * Wf
2/5MR^2 * 1rot/36.3 days = (2/5MR^2*0.590) * Wf

This needs to be squared as well, since it is part of the radius term.
 

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