Marble spiralling inside a cylinder

In summary, the conversation discusses a marble being thrown at an angle through a plastic blow-mold cylinder, and its interesting behavior of returning after reaching top dead center on the second loop. The conversation also explores the causes of this phenomenon, with some suggesting it is due to a gyroscopic effect and others questioning its plausibility. The orientation of the cylinder and the marble's motion, whether rolling or sliding, are also discussed.
  • #1
coffeenazi
1
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My son and I were playing in the park and accidently came across an interesting physical force. We threw a marble on an angle through the inside of a plastic blow-mold cylinder. The cylinder was approx 1M long X 0.6M Diameter. The marble returned after reaching top dead center on the second loop. If thrown hard enough it would spiral from one end to the other until it dropped.

We continued the excercise from each end at different speeds with the same result so long as the marble never left the surface of the cylinder.

What causes the marble to return and how? Any ideas?
Thanks!
 
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  • #2
I am having a hard time visualizing exactly what is going on. Is the cylinder axis exactly horizontal to the ground or slightly tilted? What do you mean by throwing the marble at an angle? The marbles motion in general can be broken into two components: the part along the direction cylinder's, and the part transverse to the axis. Along the axis, the marble is constrained only by friction so its motion in this direction is generally straight and constant, with a slight deceleration due to friction. Transverse to the axis, the cylinder exerts a constant inward force forcing the marble to trace out a circular orbit. The total motion is a circle in one plane plus a line along the axis, which gives you a spiral. At high speeds, gravity is negligible. At moderate speeds, gravity causes the marble to be slower at the top of its circle and faster at the bottom, like a pendulum. At low speeds, gravity overcomes the inertia of the marble which kept it pressed against the cylinder wall, and the marble falls out of its circular path. If the cylinder is perfectly horizontal, the marble will spiral away from you and not come back. If it is coming back to you, I suspect the cylinder is not horizontal and gravity is pulling it back.
 
  • #3
coffeenazi said:
My son and I were playing in the park and accidently came across an interesting physical force. We threw a marble on an angle through the inside of a plastic blow-mold cylinder. The cylinder was approx 1M long X 0.6M Diameter. The marble returned after reaching top dead center on the second loop. If thrown hard enough it would spiral from one end to the other until it dropped.

We continued the excercise from each end at different speeds with the same result so long as the marble never left the surface of the cylinder.

What causes the marble to return and how? Any ideas?
Thanks!

It is a gyroscopic affect. Linear inertia would make it go through the cylinder along a helix, but that would mean that the axis of the spin (due to rolling) has to change (rotate around the cylinder axis). The result is a torque perpendicular to the current spin axis and the cylinder axis (and thus also perpendicular to the cylinder surface at current contact point). This torque makes the marble turn around, and come back.

http://en.wikipedia.org/wiki/Gyroscope

200px-Gyroscope_wheel-text.png


[URL]http://upload.wikimedia.org/wikipedia/commons/2/26/Gyroscope_wheel_animation.gif[/URL]

If the marble was sliding, not rolling, it would move on a helix along the cylinder, and not come back.
 
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  • #4
A.T. said:
It is a gyroscopic affect. Linear inertia would make it go through the cylinder along a helix, but that would mean that the axis of the spin (due to rolling) has to change (rotate around the cylinder axis). The result is a torque perpendicular to the current spin axis and the cylinder axis (and thus also perpendicular to the cylinder surface at current contact point). This torque makes the marble turn around, and come back.
If the marble was sliding, not rolling, it would move on a helix along the cylinder, and not come back.

You are suggesting that this little glass marble massing about 20g has enough angular momentum stored that it will overcome all frictional forces to the contrary (as well as the comparatively huge kinetic energy imparted to it by the throw), and reverse its direction due to gyroscopic forces alone?

No way.
 
  • #5
coffeenazi, we need a diagram.

Or at least tell us how the cylinder was oriented.
 
  • #6
DaveC426913 said:
You are suggesting that this little glass marble massing about 20g has enough angular momentum stored that it will overcome all frictional forces to the contrary (as well as the comparatively huge kinetic energy imparted to it by the throw), and reverse its direction due to gyroscopic forces alone?
So 20g are too little for angular momentum but enough for "huge kinetic energy" ? For a rolling object the net linear momentum and the angular momentum are proportional. The same applies to kinetic energy and angular kinetic energy.

And what frictional forces does it need to overcome? It is rolling, and makes a clean turn, because the gyroscopic output torque is perpendicular to the surface.
 
  • #7
A.T. said:
So 20g are too little for angular momentum but enough for "huge kinetic energy" ?
Yes.

You spin the marble as fast as you can. I will stop it spinning with the tip of my pinkie nail.

My turn. I will throw it as hard as I can at you. You stop it with your front teeth.
 
  • #8
A.T. said:
So 20g are too little for angular momentum but enough for "huge kinetic energy" ?

DaveC426913 said:
Yes.

You spin the marble as fast as you can. I will stop it spinning with the tip of my pinkie nail.

My turn. I will throw it as hard as I can at you. You stop it with your front teeth.

We are not talking about the ability of humans to transfer different types of momentum to the marble with different body parts.

We are talking about a rolling marble. For a rolling object the net linear momentum and the angular momentum are bound to each other.
 
  • #9
A.T. said:
We are talking about a rolling marble. For a rolling object the net linear momentum and the angular momentum are bound to each other.
I think you're talking about too ideal a case. The marble might be bouncing and skidding as much as it might be rolling. The OP did say it performed two loops, and it is a cylinder 60cm in diameter. It is moving way too fast for any gyroscopic motion to come into play.
 
  • #10
DaveC426913 said:
I think you're talking about too ideal a case.
On the contrary - ignoring the spin is idealsing too much.

DaveC426913 said:
The marble might be bouncing and skidding as much as it might be rolling.

The marble reverses its linear momentum along the cylinder axis, and comes back. You know, the linear momentum that is so huge that it would knock out my teeth. If there is so much momentum transfer between the marble and the cylinder, there must be enough traction to make it spin so it mostly rolls.

DaveC426913 said:
It is moving way too fast for any gyroscopic motion to come into play.
Well, that is easy to test: Throw something into a cylinder, that doesn't roll. A coin sliding on its flat surface for example. I expect it to do a helix.
 
  • #11
I'm afraid I must withhold further speculation until I see a diagram or at least a better description.

We don't know what he's experiencing or describing. We're all talking out of our hats. For all we know the cylinder is inclined at 45 degrees. Then we'd feel pretty silly trying to use gyroscopic motion to ratinoalize why the coin came back... :biggrin:
 
  • #12
Here is a demonstration on this:
http://demonstrations.wolfram.com/RollingBallInsideACylinder/

They consider a vertical cylinder, where without disspative forces the rolling ball thrown in from the top, would go up and down and never reach the bottom end. The same applies to a horizontal cylinder. The torque perpendicular to the surface at contact point, that makes the ball turn around is called "Coriolis torque".

They also give this reference:
http://ajp.aapt.org/resource/1/ajpias/v74/i6/p497_s1 [Broken]
 
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  • #13
DaveC426913 said:
For all we know the cylinder is inclined at 45 degrees. Then we'd feel pretty silly trying to use gyroscopic motion to ratinoalize why the coin came back...
But if you throw the ball from the top and it still rolls back to the upper end, then you going to blame gravity for that?
 
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  • #14
A.T. said:
So 20g are too little for angular momentum but enough for "huge kinetic energy" ? For a rolling object the net linear momentum and the angular momentum are proportional. The same applies to kinetic energy and angular kinetic energy.

But the constant of proportionality will be tiny in the case of a small sphere so there will be very little rotational energy compared with the translational energy. . A large diameter wheel, on the other hand . . . .
 
  • #15
sophiecentaur said:
But the constant of proportionality will be tiny in the case of a small sphere so there will be very little rotational energy compared with the translational energy. . A large diameter wheel, on the other hand . . . .
The ratio of rotational to translational kinetic energy for an object rolling straight does not depend on the radius. For a solid sphere it is 0.4 which is neither "tiny" nor "very little".

But rolling straight is just the initial condition here. The ball soon gets a spin around the surface normal, so the ratio could get even higher. When you play around with the wolfram applet, you can get conditions where the KE due to that normal spin alone (red line) is greater than the entire remaining energy due to translation, roll rotation and gravity (blue line), in some phases of the loop:

popup_1.jpg


However, the below is closer to the situation with the marble in a big cylinder. The gravity is switched off, so it doesn't affect the motion along the cylinder axis, just like in a horizontal cylinder:

popup_3.jpg
 
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  • #16
Are you telling us that the rotational energy is not a function of the moment of inertia?
Obviously the ratio would be the same for all uniform spheres. That wasn't spelled out in the post, though.
 
  • #17
sophiecentaur said:
Are you telling us that the rotational energy is not a function of the moment of inertia?
No, I said:

"The ratio of rotational to translational kinetic energy for an object rolling straight does not depend on the radius."

sophiecentaur said:
Obviously the ratio would be the same for all uniform spheres.
If it's so obvious, then why do you point out that the sphere is small? You said:

"But the constant of proportionality will be tiny in the case of a small sphere so there will be very little rotational energy compared with the translational energy"

sophiecentaur said:
That wasn't spelled out in the post, though.

Yes, the 0.4 applies to uniform mass distribution. Since we talk about a marble I thought this was obvious. What kind of marble where you thinking about, where there is "very little rotational energy compared with the translational energy" during rolling?
 
  • #18
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.
 
  • #19
sophiecentaur said:
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.
sophiecentaur said:
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?
sophiecentaur said:
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.
 
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  • #20
A.T. said:
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.
 
  • #21
sophiecentaur said:
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:

2nuupuc.png


2dw822v.gif


Here the applet again:
http://demonstrations.wolfram.com/RollingBallInsideACylinder/
 
  • #22
Yes we can and the animations are well done.
 
  • #23
sophiecentaur said:
Yes we can and the animations are well done.
The credit goes to the makers of the applet. I just used it.
 
  • #24
yebbut you found it. Don't be bashful. And it makes the point well.
 
  • #25
  • #26
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.
 
  • #27
A.T. said:
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.

 
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  • #28
rcgldr said:
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.
 
  • #29
rcgldr said:
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.

rcgldr said:
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.


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?
 
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  • #30
A.T. said:
https://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).
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):

https://www.youtube.com/watch?v=qdBL41lUzl8 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.
 
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  • #31
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.
 
  • #32
DaveC426913 said:
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.
 
  • #33
A.T. said:
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.
 
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  • #34
DaveC426913 said:
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.

DaveC426913 said:
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?
 
  • #35
A.T. said:
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.

A.T. said:
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.
 
<h2>1. What is the concept of "marble spiralling inside a cylinder"?</h2><p>The concept of "marble spiralling inside a cylinder" refers to the motion of a marble inside a cylindrical container, where the marble follows a spiral path as it moves downward due to the force of gravity.</p><h2>2. What causes the marble to spiral inside the cylinder?</h2><p>The marble spirals inside the cylinder due to the combination of two forces: gravity pulling the marble downward and the walls of the cylinder exerting a normal force on the marble, causing it to change direction and follow a spiral path.</p><h2>3. How does the speed of the marble affect the spiral motion?</h2><p>The speed of the marble does not significantly affect the spiral motion. As long as the marble is moving downward with some initial velocity, it will continue to follow a spiral path due to the forces acting on it.</p><h2>4. Can the size or shape of the cylinder affect the spiral motion?</h2><p>Yes, the size and shape of the cylinder can affect the spiral motion of the marble. A larger or taller cylinder may allow the marble to spiral for a longer period of time before reaching the bottom, while a different shape (such as a cone or pyramid) may result in a different spiral path.</p><h2>5. How is the motion of the marble inside the cylinder related to physics?</h2><p>The motion of the marble inside the cylinder is related to physics through the principles of gravity, force, and motion. The spiral motion can be explained using Newton's laws of motion and the concept of centripetal force.</p>

1. What is the concept of "marble spiralling inside a cylinder"?

The concept of "marble spiralling inside a cylinder" refers to the motion of a marble inside a cylindrical container, where the marble follows a spiral path as it moves downward due to the force of gravity.

2. What causes the marble to spiral inside the cylinder?

The marble spirals inside the cylinder due to the combination of two forces: gravity pulling the marble downward and the walls of the cylinder exerting a normal force on the marble, causing it to change direction and follow a spiral path.

3. How does the speed of the marble affect the spiral motion?

The speed of the marble does not significantly affect the spiral motion. As long as the marble is moving downward with some initial velocity, it will continue to follow a spiral path due to the forces acting on it.

4. Can the size or shape of the cylinder affect the spiral motion?

Yes, the size and shape of the cylinder can affect the spiral motion of the marble. A larger or taller cylinder may allow the marble to spiral for a longer period of time before reaching the bottom, while a different shape (such as a cone or pyramid) may result in a different spiral path.

5. How is the motion of the marble inside the cylinder related to physics?

The motion of the marble inside the cylinder is related to physics through the principles of gravity, force, and motion. The spiral motion can be explained using Newton's laws of motion and the concept of centripetal force.

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