# Angular momentum

## Homework Statement

4 masses are attached to a rotating cross. At some point, mass 4 is detached from the cross. What will be the angular velocity w' in which the 3 remaining masses will rotate about their center of mass (with the cross, which has no mass)?

## Homework Equations

L(0)=L(of masses relative to center of mass)+L(center of mass itself relative to 0)

## The Attempt at a Solution

At first I calculated the angular momentum L1 = Iw (w is given). Next, I used the above formula, with a little addition. I calculated the angular momentum of the 3 masses relative to THEIR center of mass, calculated the angular momentum of their center of mass relative to 0 (the point where the first angular momentum was calculated, before the separation - 0), and to that I added the angular momentum of the fourth mass (which was detached) relative to 0. I then summed all three components. Meaning I got:
L2(relative to lab)=L(3 masses relative to their center of mass)+L(center of mass of 3 masses, relative to 0)+L(fourth mass, relative to 0). Then I wrote L1=L2.
I just want to know if this attempt is valid..

#### Attachments

• RotatingCrossOfMasses.gif
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## Answers and Replies

ideasrule
Homework Helper
It seems correct, but isn't the angular momentum of the masses relative to their own center of mass 0?

It seems correct, but isn't the angular momentum of the masses relative to their own center of mass 0?

Maybe I wasn't being clear, I was talking about the angular momentum of the masses relative to the center of mass of the 3 masses+cross. Anyway I solved the question, so thanks.