A Physics Puzzle: Double Circular Motion

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Discussion Overview

The discussion revolves around a physics puzzle that asks how to force a particle to move along two different circular trajectories simultaneously, specifically two non-concentric circles. The conversation explores various interpretations and examples of circular motion, including hypothetical scenarios and mechanical devices.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants suggest using a small ball or a planet as examples of particles that could exhibit double circular motion.
  • One participant humorously proposes a gum stuck on a tire of a car, while another counters that the trajectory around the roundabout is not purely circular.
  • There is a discussion about the nature of circular motion, with some arguing that perfectly circular motion is unlikely without the particle being fixed to a point.
  • A participant mentions the historical context of celestial mechanics and the concept of epicycles, noting that while they describe circular motion, they do not satisfy the puzzle's requirements.
  • Another participant emphasizes that the puzzle requires two distinct frames of reference to describe the motion as circular, even if the trajectories are not full circles.
  • One participant describes a scenario involving a ball on a merry-go-round, arguing that the trajectory appears circular from one frame of reference but is complex from another.
  • A later reply introduces a mechanical device with a roller and elbow joint, questioning whether it can produce two distinct circular paths.
  • Another participant expresses curiosity about a motion involving a dropped coin, suggesting that a body at the contact point could move along two circular trajectories.
  • One participant concludes that a specific example involving a ball being spun on a string while on a merry-go-round could indeed satisfy the puzzle's conditions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a definitive solution to the puzzle. Multiple competing views and interpretations of circular motion remain, with some examples being challenged and refined throughout the discussion.

Contextual Notes

Some participants note that the trajectories do not have to be full circles and that the definitions of circular motion may depend on the chosen frame of reference. There are also unresolved questions about the mechanical devices proposed and their ability to produce the required motion.

AlexChandler
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Describe a simple way to force a particle to move along two different circular trajectories at the same time. (Two circles that are not concentric) Hint: The trajectories do not have to be measured from the same frame of reference.

It need not be an elementary particle (could be even a small ball)
 
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AlexChandler said:
Describe a simple way to force a particle to move along two different circular trajectories at the same time. (Two circles that are not concentric) Hint: The trajectories do not have to be measured from the same frame of reference.

It need not be an elementary particle (could be even a small ball)

Or a planet?

http://faculty.fullerton.edu/cmcconnell/Planets.html#7a
 
A gum stuck on a tire of a car that keeps driving around a roundabout! :biggrin:
 
AlexChandler said:
Haha I'm sorry but I'm afraid this is not correct. :-p

Why is it not correct? Because he didn't say that the particle is sitting on the surface of the planet, and is not located at either pole?
 
He probably should've just said 'me' or 'you Mr. AlexChandler'. :biggrin:
 
berkeman said:
Why is it not correct? Because he didn't say that the particle is sitting on the surface of the planet, and is not located at either pole?

Well, it is true that planets don't orbit the Earth via epicycles. In fact, they orbit the Sun in ellipses. In fact, it would be highly unlikely to find any particle that moved freely in a perfectly circular path.

Perfectly circular motion usually requires the particle to be fixed to the point it's circling.

But the link is an example of double circular motion, even if it doesn't reflect the real motion of the planets (nor was it intended to, since the emphasis was on the history of celestial mechanics).

And it would be simple to rig a device where the axes of a spinning gyroscope were fitted into a forked frame and the frame rotated about a fixed point.
 
drizzle said:
A gum stuck on a tire of a car that keeps driving around a roundabout! :biggrin:

Hehe also a nice idea, but I'm afraid only the trajectory around the tire is circular. The trajectory around the roundabout is more like a cycloid.
 
Me on a merry go round spinning a ball on a string?

You're being picky. Strictly speaking you'll never get a perfect circle.

The above are all valid.
 
  • #10
BobG said:
But the link is an example of double circular motion, even if it doesn't reflect the real motion of the planets (nor was it intended to, since the emphasis was on the history of celestial mechanics).

And it would be simple to rig a device where the axes of a spinning gyroscope were fitted into a forked frame and the frame rotated about a fixed point.

But even if the epicycles were possible, this would not satisfy the puzzle. The epicycles would be circular trajectories measured in the frame of reference co-moving with the center of the epicycles, but the overall trajectory described from the frame of reference of the sun would not be circular at all.

Could you elaborate on the final idea you presented? I think it will also not work for a similar reason, but I do not fully understand what is meant by "fitted into a forked frame".
 
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  • #11
I think the puzzle has been somewhat misunderstood. The point is to find a forced motion such that two distinct frames of reference could accurately describe the trajectory of the particle as circular, and the two circular trajectories must not have the same point in space as a center.

The trajectories do not have to be full circles, as long as the particle moves along two distinct circular arcs for some time.
 
  • #12
JaredJames said:
Me on a merry go round spinning a ball on a string?

You're being picky. Strictly speaking you'll never get a perfect circle.

The above are all valid.

I am not being picky :-p but the above mentioned motions do not satisfy the puzzle. I apologize if it is unclear what I am asking for, but I tried to be as exact as possible in my wording.

For example, you on the merry go round: In your frame of reference, the trajectory of the ball is absolutely a circle. But from the frame of reference of the center of the merry go round, the trajectory is very complicated, actually it is the same as thing as the epicycles described before. It is not circular. There is only one circular trajectory in each of these examples.
 
  • #13
[PLAIN]http://i2.squidoocdn.com/resize/squidoo_images/250/draft_lens17687361module148542008photo_1298768215drawing1.jpg

A motion of a dropped coin led me to this example. Imagine if there's a small body in the contact point between the coin and the surface of the floor, won't that body be moving two different circular trajectories!... Actually the body should be fixed while the two references move relatively to each other... URGH! I'd like to know the answer to this question, thanks for keeping me curious.
 
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  • #14
AlexChandler said:
For example, you on the merry go round: In your frame of reference, the trajectory of the ball is absolutely a circle. But from the frame of reference of the center of the merry go round, the trajectory is very complicated, actually it is the same as thing as the epicycles described before. It is not circular. There is only one circular trajectory in each of these examples.
For example, if the ball is being spun about a horizontal axis even as the merry-go-round is rotating about a vertical axis. The center of the first frame of reference is the tip of of JaredJames' fingers holding the string. The center of the second frame is a point moving sinusoidally up and down through the axis of the merry-go-round in time with the rise and fall of the ball.
 
  • #15
Jimmy Snyder said:
For example, if the ball is being spun about a horizontal axis even as the merry-go-round is rotating about a vertical axis. The center of the first frame of reference is the tip of of JaredJames' fingers holding the string. The center of the second frame is a point moving sinusoidally up and down through the axis of the merry-go-round in time with the rise and fall of the ball.

Actually this does work. Great thinking! I thought at first that it would not work for the following reason: The oscillating frame of reference at the center of the merry go round will see that the ball moves back and forth along the circular trajectory. But actually if the merry go round is moving fast enough, the ball will only slow down in the FOR of the center of the merry go round, so the trajectory will be circular as measured from two distinct reference frames with two distinct centers. Great job! In fact I think that this answer is better than the one I had in mind. And in fact this would satisfy the puzzle even if the ball did travel back and forth along the trajectory. I am quite impressed.
 
  • #16
Well done... uh... Jimmy.
 
  • #17
My solution to the problem is illustrated in the attached picture. It is just a simple machine with a roller an an elbow joint. View the small object attached to the center of the elbow joint from the frame or reference of both points O and P. Point O is held fixed with respect to the piece of paper, and point P is moving at a constant velocity to the right.
 

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  • #18
How does that answer the question?

If I'm reading it right, it only has one rotational path of a small arc. Where's the second?
AlexChandler said:
Describe a simple way to force a particle to move along two different circular trajectories at the same time. (Two circles that are not concentric) Hint: The trajectories do not have to be measured from the same frame of reference.
 
  • #19
JaredJames said:
How does that answer the question?

If I'm reading it right, it only has one rotational path of a small arc. Where's the second?

Viewed from the frame of reference of O, the object travels along a clockwise circular trajectory. Viewed from the frame of reference of P, the object travels along a counterclockwise circular trajectory. It must do so. It remains a fixed distance from the point P. This is the definition of a circle.
 
  • #20
AlexChandler said:
Viewed from the frame of reference of O, the object travels along a clockwise circular trajectory. Viewed from the frame of reference of P, the object travels along a counterclockwise circular trajectory. It must do so. It remains a fixed distance from the point P. This is the definition of a circle.

EDIT: I see it.
 
  • #21
AlexChandler said:
In each reference frame the object moves along a trajectory that is a fixed distance from the origin of that reference frame. Also all motion takes place on the plane of the paper. Therefore the trajectory as measured from each reference frame is circular.

Yeah, I saw. See last post.

Can't say I'm impressed. Prefer the other answers (especially the planet one).
 
  • #22
JaredJames said:
Yeah, I saw. See last post.

Can't say I'm impressed. Prefer the other answers (especially the planet one).

Well actually the planet one is incorrect, unless you can point out some frame of reference that makes it correct.

But I do agree that the merry-go-round solution is quite nice. I prefer it over my solution.
 
  • #23
AlexChandler said:
Well actually the planet one is incorrect, unless you can point out some frame of reference that makes it correct.

But I do agree that the merry-go-round solution is quite nice. I prefer it over my solution.

The planet one is no different to the merry-go-round one, just imagine the planet going vertically instead of horizontally.

Regardless, it meets the criteria you laid out.
 
  • #24
JaredJames said:
The planet one is no different to the merry-go-round one, just imagine the planet going vertically instead of horizontally.

Regardless, it meets the criteria you laid out.

Yes I suppose that works then if the axis is oriented properly. Good thinking.
 
  • #25
AlexChandler said:
Well actually the planet one is incorrect, unless you can point out some frame of reference that makes it correct.

But I do agree that the merry-go-round solution is quite nice. I prefer it over my solution.
Which one you like better is simply a matter of taste. I think your solution is quite clever too. I knew the solution would involve a moving axis because three points determine a circle.
 

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