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## Homework Statement

Find the hours it takes for the Earth to rotate in one day if the mass is reduced to 2/3 of its original mass and it is shrunk to 3/4 its original size.

## Homework Equations

L=Iω

## The Attempt at a Solution

To start this problem I assumed that angular momentum is conserved from the original Earth to the final earth. This means the angular velocity must change in order for the angular momentum to remain unchanged. So used this equation: I

_{earth}ω

_{earth}=I

_{k}ω

_{k}and got that I

_{earth}ω

_{earth}/I

_{k}=ω

_{k}. I plugged in the data and got that the new speed is twice the speed of the original earth. This would mean the Earth rotates about 12 hrs a day. This SEEMS wrong but I am not sure.

Note: k is the final earth.

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