# Angular velocity $\omega$ by $v$

We have two girls, with mass (M). They become close to each other in speed of V. The distance between them is 3L.

I was asked to calclute the Angular velocity (w) of the two girls. So I set the rotation axis in the middle (where the distance between the two girls and the axis is 1.5L, and I calcute the Angular velocity by the formula of w=v\r, where r=1.5L, and I got that w=2v/3L.

As I understood, the answer is correct, but this is not the correct way. What is my mistake? (sorry about my english)

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– Adam Sh Feb 3 '12 at 22:54

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Please do not write "w" for "$\omega$" :-). You can use LaTeX math in `$...$` signs. So you can write `$\omega$`. – queueoverflow Feb 3 '12 at 23:20

## 1 Answer

They do not come closer to each other according to the picture. They always keep the distance of the $3L$ since they hold onto that bar that is going to rotate counter clockwise.

I think your answer $$\omega = \frac{2}{3} \frac{v}{L}$$ is fine. This works since $v$ and $r$ are perpendicular, with a 90° angle in between.

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But I have one problem with my answer: If I would set the rotation axis in a distance of 2/3 fron the one, and 1/3 from the other - meaning from one girl the distance is L and from the second, the distance is 2L. I would get a diffrent $w$. My way is working beacuse we are talking on center of mass? – Adam Sh Feb 4 '12 at 7:57
Yes, the symmetry says that they rotate around the center. If one girl is faster than the other, they will have different $\omega$, that is true. – queueoverflow Feb 4 '12 at 14:38
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