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## Homework Statement

Spinning Space Ship

One way to provide artiﬁcial gravity (i.e., a feeling of weight) on long space voyages is to separate a spacecraft into two parts at the ends of a long cable, and set them rotating around each other. A craft has been separated into two parts with a mass of 86000 kg each, at the ends of a cable with their centers of mass 106 m apart, rotating around the center point of the cable with a period of 232.2 seconds.

If the cable is reeled in so that the the centers of the two pieces are now only 74.2 m apart, what will the new period be?

## Homework Equations

T = 1/f or f = 1/T

ω = 2*pi*f

L = I*ω

I = Ʃ m*r^2

L(initial) = L(final)

## The Attempt at a Solution

First, I noted that this scenario should follow the principle of conservation of angualr momentum. Therefore L(initial) = L(final) should be true. Then, I followed this series of steps...

L = I*ω

L = (Ʃ m*r^2)*ω

L = (2*(m*r^2))*ω

L = (2*(m*r^2))*2*pi*f

L = (2*(m*r^2))*2*pi*1/T

Upon finding this initial angular momentum, I thought I could find the final L by setting this expression equal to L(final) with the new radius to the axis point and with T set as an unknown variable.

Please let me know if this is on the right track? I am a little bit hesitant about it so any feedback would be awesome.