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ME101

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I'm a UG in mechanical engineering and I've a basic understanding of (but a very keen interest in) physics.

Before I get started, I just want to say that this is not my homework.

So there's this problem that's been in my head for a while. I don't know enough physics to solve it so I came here to seek help. Thanks to anyone who responds.

There are two masses (m1 and m2, say) that can rotate about an axis. m1 is at a distance of r1 from the axis and m2 at r2. I know, this is one of the most common problems in simple physics.

The condition here is m1 and m2 are

**not equal**and neither are r1 and r2.

Once given an initial velocity, can there be a condition in which the masses keep rotating (forever) about the axis? I don't want you guys to solve the problem, just give me the considerations I should take into account to solve it.

1 thing I found out was that the center of mass of the system needs to be above the axis of rotation at all times, right?

Thanks for any/all help offered. Have a great day. :)