This problem's been bothering me for a while now

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Discussion Overview

The discussion revolves around a mechanical engineering student's inquiry into the conditions under which two unequal masses can rotate indefinitely about an axis, considering factors such as initial velocity and the position of the center of mass. The conversation explores both theoretical aspects and the implications of gravity on the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster (OP) questions whether two unequal masses can rotate indefinitely about an axis given an initial velocity, seeking considerations rather than solutions.
  • One participant suggests that the center of mass must remain on the axis of rotation for perpetual motion to be possible.
  • Another participant introduces the idea that if gravity is considered, it could influence the motion of the masses, questioning if gravity could facilitate continuous rotation.
  • A different participant expresses skepticism about the feasibility of the OP's idea, stating that gravity would cause the center of mass to fall, complicating the notion of perpetual motion.
  • A later reply cites forum rules against discussions of perpetual motion machines, indicating that such concepts are not permitted in the forum.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of the proposed system, with some questioning the possibility of perpetual motion under the influence of gravity, while others clarify the conditions necessary for rotation. The discussion remains unresolved regarding the viability of the OP's concept.

Contextual Notes

The discussion touches on the principles of physics, including Newton's laws and the concept of the center of mass, but lacks consensus on the implications of gravity and the possibility of perpetual motion. The mention of forum rules indicates a limitation on the scope of the discussion regarding perpetual motion machines.

ME101
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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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Hi ME101! Welcome to PF! :smile:
ME101 said:
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. :wink:

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. :smile:​
 
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. :)
 
Hi ME101! :smile:
ME101 said:
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. :confused:​
 
ME101 said:
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.

Discussions of Perpetual Motion Machines (PMMs) are not allowed here -- they are on the Forbidden Topics list in the PF Rules (see Site Info at the top of the page):

PF Banned Topics said:
Pseudoscience, such as (but not limited to):

Perpetual motion and "free energy" discussions
http://wiki.4hv.org/index.php/Free_Energy_Debunking
http://en.wikipedia.org/wiki/Perpetual_motion
http://www.skepdic.com/freeenergy.html
http://www.skepdic.com/perpetual.html

Please follow those links to see why what you are thinking about will not work.

This thread is closed.
 

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