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Author Topic: The turntable paradox  (Read 1819 times)

ortwin

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Re: The turntable paradox
« Reply #15 on: November 30, 2022, 02:56:59 PM »

....  If I find a simple way to simulate a turntable, ...
Maybe you have an old record player sitting somewhere?
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In the broader world of tops, nothing's everything!  —  Jeremy McCreary

ortwin

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Re: The turntable paradox
« Reply #16 on: November 30, 2022, 03:23:48 PM »

...
Still astounded that this negative feedback manages to bring the rotation and translation to a halt at exactly the same instant ...
The separation of that movement into spin and translation is nothing but a mathematical trick. It is easier for us to treat it and grasp it that way,  but if you think about it from the perspective of some particles of the surface of the table, at any given moment in time, there is just something sliding over it  with some speed in some direction.  How should those particles know how we want to separate the movement? How should they know which part of the movement they should slow down faster so that only what we call "translation" or "spin" ist left over at the end?
Its just "the" movement that comes to a halt.



« Last Edit: November 30, 2022, 04:47:22 PM by ortwin »
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ta0

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Re: The turntable paradox
« Reply #17 on: November 30, 2022, 07:06:12 PM »

I thought about it a bit and ended up by not understanding why that is "astoundingly".

I guess I'm easily astounded. And as my sig might suggest, I like it that way.

Quote
Everything in the world is strange and marvelous to well-open eyes.
  -- Jose Ortega y Gasset

I'm with Jeremy on this one. Although the qualitative explanation is plausible and makes sense, it's still outstanding that you can rotate a disk in place with zero displacement and you can also slide a disk with zero rotation, but if you simultaneously rotate and slide a disk, it will stop rotating and sliding at the same time.

For easy reference, the paper can be downloaded here: https://arxiv.org/abs/physics/0210024
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ortwin

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Re: The turntable paradox
« Reply #18 on: December 01, 2022, 02:31:37 AM »

...
I'm with Jeremy on this one. Although the qualitative explanation is plausible and makes sense, it's still outstanding that you can rotate a disk in place with zero displacement and you can also slide a disk with zero rotation, but if you simultaneously rotate and slide a disk, it will stop rotating and sliding at the same time....
Oh, I like it that we have this controversial, almost philosophical, discussion!
I still think that much of the astonishment (that I can definitely relate to, to a certain degree) comes from the bias induced by separating the movement into "sliding" and "rotating". Just because we can describe a movement this way, does not mean that the separation has physical sense beyond making it easier to handle the problem mathematically.
Let's look only at the sliding motion for a minute:
Consider the disk only sliding along on a surface/plane in a straight line starting with some arbitrary velocity ax + by in our coordinate system where we chose the  directions of x and y as we thought convenient. Is it not very peculiar now, that the movement in the direction of x always stops (due to friction) at the exact same time as the movement in the direction of y ??





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ta0

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Re: The turntable paradox
« Reply #19 on: December 01, 2022, 09:29:02 AM »

Consider the disk only sliding along on a surface/plane in a straight line starting with some arbitrary velocity ax + by in our coordinate system where we chose the  directions of x and y as we thought convenient. Is it not very peculiar now, that the movement in the direction of x always stops (due to friction) at the exact same time as the movement in the direction of y ?
But in your thought experiment, the driving force for the x and y is the same: the linear momentum. On the other hand, for the sliding and rotating disc, the sliding is powered by the linear momentum (proportional to the mass and linear speed) while the rotation is powered by the angular momentum (proportional to the moment of inertia and angular speed).

By the way, I believe this phenomenon would work for any object, not just a disc. But I guess the final ratio between the linear speed and angular speed would change. According to the paper, for the disc ε0 = v/Rω is a constant approximately equal to 0.653. It would be interesting to measure it for cylinders, tubes and cones of different height but same radius.

« Last Edit: December 01, 2022, 09:59:41 AM by ta0 »
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ortwin

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Re: The turntable paradox
« Reply #20 on: December 01, 2022, 11:56:02 AM »

...But in your thought experiment, the driving force for the x and y is the same: the linear momentum. On the other hand, for the sliding and rotating disc, the sliding is powered by the linear momentum (proportional to the mass and linear speed) while the rotation is powered by the angular momentum (proportional to the moment of inertia and angular speed)....
But the "driving force" of sliding and rotation is in fact the same. When you look up how one arrives at the "angular momentum" you can see that is just a clever summation/integration of the  little linear momenta of the constituting particles. There is no special physics for rotation, only Newton's laws summed up in ways so that you get similar looking laws as for linear movement. All special laws, forces and effects we know and love in tops and other rotating things, can be viewed as "emergent effects" based on Newtons laws (I think).
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ta0

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Re: The turntable paradox
« Reply #21 on: December 01, 2022, 01:46:34 PM »

But the "driving force" of sliding and rotation is in fact the same. When you look up how one arrives at the "angular momentum" you can see that is just a clever summation/integration of the  little linear momenta of the constituting particles. There is no special physics for rotation, only Newton's laws summed up in ways so that you get similar looking laws as for linear movement. All special laws, forces and effects we know and love in tops and other rotating things, can be viewed as "emergent effects" based on Newtons laws (I think).
All that's true, but the "emergent effects" can be very surprising as we well know on this forum.
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Iacopo

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Re: The turntable paradox
« Reply #22 on: December 01, 2022, 03:41:30 PM »

Maybe you have an old record player sitting somewhere?

If I had it, it would have been the simplest solution, but I don't.
I tried with the glass pane. It was more difficult than I thought.
The main problem are the surfaces, the glass is too slippery and the tested discs slip far too much. The tested ball instead seems not smooth enough, (the noise while it rolls tells it), so its trajectory, especially when it rolls slowly, is not accurate.
I could observe some stationary rolling.
The stationary rolling is not stable, when the ball slows down a bit, (rolling resistance), it starts to move in circles.
The circles tend to be larger and larger, until falling down from the pane.
The center of these circles tended to shift towards the center of the glass pane, making difficult to observe the ball circling at a side of the center of the glass pane.   

https://www.youtube.com/watch?v=otoy3FpHoKQ
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jim in paris

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Re: The turntable paradox
« Reply #23 on: December 04, 2022, 02:41:19 AM »

oh oh
very cool set up iacopo,

even if the ball goes away , at least it creates a nice sound
I have a regular turntable 33 or 45 rpm
i wonder which speed would be most suitable for an experiment?

ciao for now

jim
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Iacopo

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Re: The turntable paradox
« Reply #24 on: December 04, 2022, 12:15:08 PM »

oh oh
very cool set up iacopo,

even if the ball goes away , at least it creates a nice sound
I have a regular turntable 33 or 45 rpm
i wonder which speed would be most suitable for an experiment?

ciao for now

jim

Thank you, Jim.  I am not sure about the optimal speed; in my case, it was difficult with the glass pane spinning fast, because I had to throw the ball without hitting with my hand the strings to which the pane was attached, but you don't have this problem, with the turntable. Maybe, also, the ball could slip towards the outside, if the speed is too high.  On the other hand, I noticed that if the pane rotates too slowly, the ball also moves more slowly, and especially when the ball goes towards the center of the rotating plane, where the speeds are lowest, the ball at that point can stop to move completely and stand still, or it can move very slowly and a bit randomly in direction, because of the tiny irregularities of the surfaces, to which the ball is sensitive especially at the lowest speeds.

One interesting thing that I noticed is that, in the fourth sequence, the ball could make two revolutions staying at a side of the center of the glass pane, and in that situation the ratio between the rotational speed of the pane and that of the revolutions of the ball was about 7:2, as explained before in the thread. Intriguing.
« Last Edit: December 04, 2022, 12:20:22 PM by Iacopo »
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Pepe

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Re: The turntable paradox
« Reply #25 on: December 21, 2022, 09:16:34 AM »

I love this discussion so interesting and visually mesmerizing
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