marble spiralling inside a cylinder


by coffeenazi
Tags: cylinder, inside, marble, spiralling
A.T.
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#19
Aug17-11, 06:07 AM
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Quote Quote by sophiecentaur View Post
It would be quite possible to imaging a marble which was a hollow sphere and then things would be different. (The ratio would be 1, I think)
No, it would be 2/3.
Quote Quote by sophiecentaur View Post
Or a sphere with a lot of mass at the centre,
We talking about a marble here. Why would one assume such a non-uniform mass distribution?
Quote Quote by sophiecentaur View Post
The phrase 'uniform sphere' doesn't cost much to write and gives helpful precision.
I said 'solid sphere', and from the context (marble) it was obvious that I meant uniform density.

If you are so much into precision in language then you should have specified what mass distribution you assumed where the ratio is tiny, because it had obviously nothing to do with the marble discussed here. Instead you mentioned the size, which is irrelevant for the ratio.
sophiecentaur
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#20
Aug17-11, 06:17 AM
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Quote Quote by A.T. View Post
No it would not be 2/3.


If you are so much into precision in language then you should have specified what mass distribution you assumed where the ratio is tiny, because it had obviously nothing to do with the marble discussed here. Instead you mentioned the size, which is irrelevant for the ratio.
Yes - 2/3. I was thinking of a circle - not a spherical shell - durr.

Yes - I agree that size of similar objects has no bearing on it.
A.T.
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#21
Aug17-11, 04:20 PM
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Quote Quote by sophiecentaur View Post
Yes - I agree that size of similar objects has no bearing on it.
I hope we also all finally agree that the angular kinetic energy of a rolling marble is not negligible compared to its linear kinetic energy. And that gyroscopic effects play a role here. I chose some parameters closer to the description in the OP:





Here the applet again:
http://demonstrations.wolfram.com/Ro...sideACylinder/
sophiecentaur
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#22
Aug17-11, 04:44 PM
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Yes we can and the animations are well done.
A.T.
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#23
Aug17-11, 05:00 PM
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Quote Quote by sophiecentaur View Post
Yes we can and the animations are well done.
The credit goes to the makers of the applet. I just used it.
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#24
Aug17-11, 05:10 PM
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yebbut you found it. Don't be bashful. And it makes the point well.
A.T.
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#25
Aug21-11, 02:43 AM
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Here an experiment on this. In the second attempt the ball jumps back out, against gravity. Returning from a horizontal cylinder would be much simpler.



More info:
http://www2.eng.cam.ac.uk/~hemh/movi...ballincylinder
DaveC426913
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#26
Aug21-11, 11:01 AM
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Man, when you're right you're right.

I'd never heard of such a phenomenon but I'm sure aware of it now.

Hat's off.
rcgldr
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#27
Aug21-11, 03:15 PM
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Quote Quote by A.T. View Post
Here an experiment on this.
That ball appears to be similar to a "superball", high coefficient of friction and very elastic (most of the energy conserved) in both shear and compression. I'm wondering if the reaction is similar in principle to when that type of ball is bounced under a table and returns instead of going out the other side.

http://www.youtube.com/watch?v=e-Skl2Z1wkg
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#28
Aug21-11, 03:21 PM
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Quote Quote by rcgldr View Post
That ball appears to be similar to a "superball", high coefficient of friction and very elastic
This was what threw me in the first place. I simply could not believe that a glass marble could engage with the cylinder well enough to cause it to reverse its course. It's counter-intuitive.

But A.T.'s demos correlate so spectacularly with the observation of the OP that I'd say it's pretty much the final word on this thread.
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#29
Aug22-11, 07:54 AM
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Quote Quote by rcgldr View Post
That ball appears to be similar to a "superball", high coefficient of friction and very elastic (most of the energy conserved) in both shear and compression.
The author of the video recommends using the ball from a computer mouse (rubber coated steel). They have high friction but are not very elastic. For the gyro effect you want them to roll, not to bounce around.

Quote Quote by rcgldr View Post
I'm wondering if the reaction is similar in principle to when that type of ball is bounced under a table and returns instead of going out the other side.

http://www.youtube.com/watch?v=e-Skl2Z1wkg
Here you of course do need elasticity. And it is basically a 2D scenario, where the gyro effect doesn't play a role. The question is if such a bouncing ball could also come back from a horizontal tunnel (with a round or squared cross section) when thrown in with a circumferential velocity component about the tunnel axis (so it bounces around the axis). After all, it seems that rolling in a cylinder could also be approximated as many small bounces?
A.T.
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#30
Aug25-11, 03:04 PM
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Quote Quote by A.T.


Here you of course do need elasticity. And it is basically a 2D scenario, where the gyro effect doesn't play a role. The question is if such a bouncing ball could also come back from a horizontal tunnel (with a round or squared cross section) when thrown in with a circumferential velocity component about the tunnel axis (so it bounces around the axis).
I tried it, and as expected the ball came back consistently, after 3-5 bounces. I even hit the camera by accident. Here the video (it's a cheap camera at only 30fps so you have to watch closely):




This bounce version is basically a discretized version of rolling in a cylinder. Here the momentum is transferred in a few discrete steps. It might be simpler to explain/understand than the contious rolling case.
DaveC426913
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#31
Aug25-11, 05:23 PM
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I have no doubt that a superball can turn itself around. Anyone who's ever played with one can get it to spin off in wild directions. It's the whole point of a superball. Lot of mass, lot of friction.

I still do not see how one could ever do that with a glass marble.
A.T.
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#32
Aug26-11, 06:31 AM
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Quote Quote by DaveC426913 View Post
I still do not see how one could ever do that with a glass marble.
In a horizontal plastic cylinder I see no problem. But you would need a professional high-speed camera to film it.
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#33
Aug26-11, 08:18 AM
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Quote Quote by A.T. View Post
In a horizontal plastic cylinder I see no problem. But you would need a professional high-speed camera to film it.
I believe there are two forces in contention; one is gyroscopy, the other is "English".

If I toss a superball at the ground, I get get it to do all sorts of tricks by playing with its spin. Effectively, I am applying English. Gyroscopy is one thing, but asymmetric reflection is another (because the spinning superball has grip).


I just don't think it is possible to have a glass marble provide grip. A marble would not bounce back out of a box, because it will not be able to apply that force during contact.
A.T.
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#34
Aug26-11, 08:46 AM
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Quote Quote by DaveC426913 View Post
Gyroscopy is one thing, but asymmetric reflection is another (because the spinning superball has grip).
I don't think there is a fundamental difference. It's all just conservation of angular momentum. The rolling case is just more continuous than the bouncing case : Many infinitesimally small bounces.

Quote Quote by DaveC426913 View Post
A marble would not bounce back out of a box; because it will not be able to apply that force during contact.
Bouncing back from a square box, no. Rolling back from a plastic cylinder, possibly. It depends on the surface properties of the plastic.

If you throw a glass marble along a smooth plastic floor it starts rolling pretty quickly. So it does have enough traction, otherwise it would just slide. Why should it not roll in a cylinder?
DaveC426913
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#35
Aug26-11, 09:37 AM
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Quote Quote by A.T. View Post
I don't think there is a fundamental difference. It's all just conservation of angular momentum. The rolling case is just more continuous than the bouncing case : Many infinitesimally small bounces.
No it isn't. The superball is changing its course by applying its own spin to the surface and meeting resistance.

Quote Quote by A.T. View Post
Bouncing back from a square box, no. Rolling back from a plastic cylinder, possibly. It depends on the surface properties of the plastic.

If you throw a glass marble along a smooth plastic floor it starts rolling pretty quickly. So it does have enough traction, otherwise it would just slide. Why should it not roll in a cylinder?
It will roll - but its rotation will not then transfer back into motion. If I give it a high spin as I throw it at the ground, it will not jump to the left like the superball will. The marble cannot transfer its own angular momentum through friction into a course change during the infinitesimal time it is in contact with a surface.

You've re-befuddled the issue by introducing the spurious example of the square box.
A.T.
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#36
Aug26-11, 09:53 AM
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Quote Quote by DaveC426913 View Post
The superball is changing its course by applying its own spin to the surface and meeting resistance.
The same happens with the ball rolling in a cylinder. Just continuously: infinite number of infinitesimally small course changes, with the same net effect.

Quote Quote by DaveC426913 View Post
You've re-befuddled the issue by introducing the spurious example of the square box.
One could use a hexagonal box, or an octagonal box. Or let the number of sides (and bounces per cycle) go to infinity, then you have rolling in a cylinder.

Quote Quote by DaveC426913 View Post
It will roll - but its rotation will not then transfer back into motion.
This doesn't make sense. If it has enough traction to transfer motion into rotation (start rolling), why should it not have enough traction to transfer rotation back into motion (change course)?


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