marble spiralling inside a cylinder

sophiecentaur

If I got hold of the wrong end of the stick then so could someone else. 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) Or a sphere with a lot of mass at the centre, where the ratio could be as small as you like.
Also there is an earlier post with a diagram of discs - which have a different MI from that of a sphere. The phrase 'uniform sphere' doesn't cost much to write and gives helpful precision. That's all but perhaps I was being too picky.

A.T.

No, it would be 2/3.
We talking about a marble here. Why would one assume such a non-uniform mass distribution?
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

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.

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

Yes we can and the animations are well done.

A.T.

The credit goes to the makers of the applet. I just used it.

sophiecentaur

yebbut you found it. Don't be bashful. And it makes the point well.

A.T.

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

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

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

DaveC426913

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.

A.T.

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.

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.

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

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.

In a horizontal plastic cylinder I see no problem. But you would need a professional high-speed camera to film it.

DaveC426913

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.

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.

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?