Tippe top; some observations, and an attempt to explain its behaviour

[Iacopo]

Tippe top spinning on rubber surface

This is the experiment I mentioned at the beginning of the thread.

I thought to observe the behaviour of the tippe top spinning on an anti-slip surface, if something useful for to understand its behaviour would come out.

I tried to spin the top on a silicon rubber surface. But the grip was too high, the top moves chaotically on it.
I reduced a bit the grip by rubbing a tiny amount of talcum powder on the silicon surface.
I could adjust the grip by adding less or more talcum powder. I wanted the surface with the highest grip, but on which the top could still spin smoothly.

That was the spinning surface I used in the video below.
The grip was still high, the top could spin on it for only a few seconds before to stop, while spinning on glass the same top can spin for two minutes or more.

[Iacopo]

These are the data of the top in the video above:

[Iacopo]

Because of the high grip, the top slowed down rapidly. Il lost 700 RPM in only half a second, (the rising center of mass was a cause too, but the high grip was certainly the main cause).

The reversal of the top also was very rapid; it went from 12° to 120° in half a second.
About four times faster than spinning on glass.
Not too surprisingly, the higher friction makes the reversal faster.
The reversal on the rubber was never complete: when the stem touched the ground, the top had already lost so much speed that it had no more sufficient energy for to complete the tip-over.

[Iacopo]

But my attention was especially caught by something else:
looking at the video, it can be seen that there is a misalignment of the top relatively to the green reference lines, as the top spins. It is centerd in the green lines when we see the bottom of the top, and it is shifted to the left when we see the spindle. The images below are two frames from the video for to better show the effect. This means that the rotation axis is no more centered on the center of mass but a bit shifted out of it.

[ortwin]

Iacopo, for me the video link you posted on 23rd of march at 10:05 am is not working. Maybe ir has something to do with the site being down for a few days. I guess this is the video?

https://www.youtube.com/watch?v=bzy_hUg ... Z3Voc2c%3D

[Iacopo]

Iacopo, for me the video link you posted on 23rd of march at 10:05 am is not working.

Now it works.. I bet Ta0 made something. Thank you, Ta0.

[Iacopo]

I took all the measurements and reported the positions of CM, CP and R, in scale, in the photo below.
The top is shown from above, when the stem is tilted by 90°.
The diameter of the top is mm 29.2
CP-CM distance is mm 2.3
The rotation axis results shifted not only sideways but also towards the contact point.
The distance between the rotation axis and the center of mass is 0.5-0.7 mm.



Is this off centered rotation axis a random coincidence ?
It doesn't seem so, even analyzing the second sequence of the last posted video, the result was about the same.
Same shift, in the same direction.

But I don't think that this should be considered strange: the strong deceleration together with the unbalance of this particular top when it spins in tilted position, coud be responsible of the shift of the rotation axis.
I started wondering, why the rotation axis moves to that side ? And, above all, why does it shift towards the contact point ?

[Iacopo]

I made a side experiment for to try to shed some light on this issue:

I made a top with three tips, evenly spaced, and at the same distance from the center of the top, (photo below).
Two tips are made of slippery teflon and one tip is made of rubber;

[Iacopo]

I spun this top on the table and made a video for to check the position of the rotation axis at the various speeds.

This is the video. The rubber tip, in the video, is in the sector of the top where there is a bit larger piece of white adhesive tape with marks of a red pen.

[Iacopo]

This top can't be spun too fast because it becomes unstable.
At the highest speed, the rotation axis is near the center of mass. If it could spin faster, I suppose that it would spin just about the center of mass, or very near to it.
At the decreasing of the speed, the rotation axis shifts sideways, (the same side as in the tippe top), and, more and more, towards the rubber tip.
At slow speed, the rotation axis passes through the rubber tip.

[Iacopo]

I believe that both the rubber tip and the center of mass want to stay in the rotation axis, the first one by means of friction, the second one by means of inertia.

But they can't stay both in the rotation axis at the same time, so there is a fight between them;

at high speed, the inertial forces prevail so the top spins about the center of mass or close to it.
At low speed, the inertial forces become weak, so the top spins about the rubber tip.

[ta0]

I find it intuitive that the top would spin around the center of mass for a frictionless surface but would shift towards the contact point when there is friction.
I look forward to the resto of your explanation. I always admire your experimental skills.

[Iacopo]

I find it intuitive that the top would spin around the center of mass for a frictionless surface but would shift towards the contact point when there is friction.

I too find it intuitive, but I need to afford this issue a bit more in depth.
Tomorrow I will expose another experiment, before to say what I think that happens in tops and in the tippe top.

[Iacopo]

In this experiment there is a disc spinning on the lathe, then there is an elastic thin rod, attached to the tool post and orthogonal to the surface of the disc. When the thin rod is moved towards the disc until touching it, the friction bends the thin rod until its end reaches the center of the disc.

More tests and thinking would be needed for to better understand the dynamics, but, again, we see that friction moves the contact point towards the rotation axis, like in the top with three tips: this is not very intuitive, because the friction force is not directed there, anyway this is what it happens.



In the second part of the video, a ball suspended to an elastic thin rod spins off centered from the rotation axis: the ball bends the rod for to move towards the rotation axis and stay there, meaning that it is able to exert a force on the system for to do so.



I believe that, in spinning tops, both the center of mass and the contact point always try to move towards the rotation axis and stay there, unless something particular prevents them to do so.

[Iacopo]

This is how this strongly unbalanced top spins:

the center of mass moves towards the rotation axis and stays there while the top spins.
The contact point too stays in the rotation axis.
As a result, the top tilts, and spins in tilted position.



Here is the spin in slow motion: