Period of Star When Diameter Shrinks

In summary, the mass of a star is 1.370×1031 kg and it performs one rotation in 38.10 days. If its diameter suddenly shrinks to 0.330 times its present size, its new period (in days) can be found using the equation 1/38.1 = 0.330^2/x, where x represents the new period in days. Solving for x gives a value of approximately 2198.249 days.
  • #1
7
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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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  • #2
Take care of the units. rot/day is not second.

ehild
 
  • #3
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?
 
  • #4
wi and wf have the same units.

ehild
 
  • #5
it asks for the new period in days! I am not sure what to do with this problem
 
  • #6
I am getting like 2198.249 as an answer.
 
  • #7
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
 
  • #8
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
 

1. What is the "Period of Star When Diameter Shrinks"?

The "Period of Star When Diameter Shrinks" refers to the phase in a star's life cycle where it begins to shrink in size due to the depletion of its nuclear fuel.

2. How does a star's diameter shrink during this period?

As a star's nuclear fuel is used up, the energy production in its core decreases, causing the core to contract. This results in a decrease in pressure and temperature, causing the outer layers of the star to collapse inward. This contraction causes the star's diameter to shrink.

3. What happens to a star's temperature during the "Period of Star When Diameter Shrinks"?

As the star's diameter decreases, the energy produced in its core becomes more concentrated, leading to an increase in temperature. This increase in temperature can cause the outer layers of the star to expand, counteracting the shrinking of the diameter.

4. How long does the "Period of Star When Diameter Shrinks" last?

The duration of this period varies depending on the initial mass of the star. Smaller stars, such as red dwarfs, can stay in this phase for trillions of years, while larger stars, such as red giants, may only experience it for a few million years.

5. What is the significance of the "Period of Star When Diameter Shrinks"?

This period marks a crucial stage in a star's evolution, as it signals the end of its main sequence life and the beginning of its transformation into a different type of star. It is also essential for the formation of new stars, as the shrinking of a star's diameter can trigger the collapse of nearby gas and dust, leading to the birth of new stars.

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