# This problem's been bothering me for a while now

by ME101
Tags: bothering
 P: 4 Hi, newbie here. 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. :)
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P: 26,148
Hi ME101! Welcome to PF!
 Quote by ME101 Once given an initial velocity, can there be a condition in which the masses keep rotating (forever) about the axis? … 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?
Yes, except you mean it needs to be on the axis of rotation … the axis is a line, and the centre of mass needs to be on that line.

The two principles of physics that you need are good ol' Newton's first law, and the principal axes of a rotating body.

Since you want the masses to rotate forever about the axis, that means the centre of mass must either rotate forever about the axis or must stay forever on the axis.

From Newton's first law, if there are no external forces on the system (ie, after you start it you just let it carry on), then the centre of mass must move at a fixed speed in a fixed direction (or be stationary) …
so rotating about the axis is not possible.
A rotating body can only rotate without wobbling (precessing) if it is rotating about a "principal axis" of the body.

The principal axes of your two masses are the line joining them, and any line perpendicular to them (through the centre of mass) …
so the two masses must be lined up either along the axis of rotation (so they're just spinning on the spot), or perpendicular to it.
 P: 4 You talked about a system that is statically balanced, right? Now what if, the effect of gravity is considered? So what I want is, I want gravity to be rotating the masses such that the mass at the top always tends to move down, driving the lower mass up and the loop continues.... forever. Is that possible? Thanks again. :)
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P: 26,148
This problem's been bothering me for a while now

Hi ME101!
 Quote by ME101 Now what if, the effect of gravity is considered? So what I want is, I want gravity to be rotating the masses such that the mass at the top always tends to move down, driving the lower mass up and the loop continues.... forever.
I don't think I understand …
gravity will make the centre of mass fall (increasingly fast) for ever.
Mentor
P: 41,109
 Quote by ME101 You talked about a system that is statically balanced, right? Now what if, the effect of gravity is considered? So what I want is, I want gravity to be rotating the masses such that the mass at the top always tends to move down, driving the lower mass up and the loop continues.... forever. Is that possible? Thanks again. :)
Welcome to the PF, ME101.

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