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This is going to be one of the most childish questions ever asked on this site but hear me out.

Today, as I'm fiddling around with balls and toilet rolls (as one does), I found something interesting that I couldn't quite explain.

So first, there is an inclined plane, a heavy metal ball, and also a used toilet roll, a little rough, but the surface of the table is smooth.

When I was done rolling balls up and down, I thought that "Hey, I should put the ball in the roll and just see what happens."

This is when something very interesting happens. (at least to me, not a physics major, all my knowledge is limited to algebra-based physics, I know.)

The metal ball does not leave the cylinder when it rolls down at a slightly slanted angle. By that I mean I just release it, no initial velocity, and maybe at a 5 or 7-degree angle down the ramp. It just goes near the rim of the toilet roll, pokes out a little bit, and then back.

When I started to push it, it reaches the hole, stays there for 1 second or so, and falls off.

Now I know there's definitely something funny going on with kinetic rotational motion, friction, or momentum going on here, but is there maybe a formula, or an effect that wraps up this "phenomenon?"

If you could somehow calculate this, just make up your own numbers.

Again, the list:

A heavy metal ball -Now a smooth marble glass ball.

A used toilet roll -Now a smooth glass slide that acts as the cylinder

Inclined ramp -IMPORTANT: No longer needs a ramp, any flat surface will do if added initial velocity.

Released it at an angle down the ramp, turning left/right 5-7 degrees will all make this happen -Same thing, the angle doesn't matter and it works either way.

SIDE VIEW: https://i.imgur.com/dSbAvoy.png

AERIAL VIEW: https://i.imgur.com/mGMqACP.png

I switched to PS for aerial hence the font change, don't ask. Hope this helps.

Using a guitar slide and glass marble on my flat floor. It also "peeks" out! I don't have a convenient smooth ramp at my disposal so that might have to wait. But the important thing is that angle no longer matters! With (hopefully) minimum friction I think a lot of things will get clearer rather than the rough toilet roll.

I've tried it out on the smoothest surface I could find and it is still doing the same thing.

Ball and cylinder: https://i.imgur.com/7vyXAkD.jpg, Also shows what it looks like by "peeking out." I'm gonna get laughed at so hard, but I really want to know. Thanks!

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I do not know whether this is directly relevent to what you are seeing, but balls rolling in cylinders are known to have some weird behaviour. The famous and most infuriating example occurs in Golf where the ball goes down into the hole, rolls round a complete circuit and pops out again. (I.e in $\to$ out, rather than your out $\to$ in). There is a cute demo and description of this at https://demonstrations.wolfram.com/RollingBallInsideACylinder/

I gather that this used to be a notoriously tricky exam problem. It is discussed on page 27 of J. E. Littlewood's "mathematician's miscellany" along with examples of ball rolling on cylinders.

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