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[Iacopo]

This is the tipped ring; in the video below, we can see in slow motion its movement after the release.
I show only the tilting movement, not the spinning about the vertical axis, to make more evident the movement of the center of mass, (the red dot), relatively to the spin axis, (the green line).

The centrifugal force pulls the center of mass away from the rotation axis, but the ring is spinning in counterphase, (since its TMI_tip is larger than the AMI), so the effect is that the CM moves towards the rotation axis instead of getting away from it.

More intuitively, we could think to it like the ring wanting to spin about its center of mass; the tip is far enough from the CM so it can't prevent the ring from doing so.

The rotation axis passes through the tip, and the CM moving towards the rotation axis makes the ring to tilt, until the CM reaches it. During the tilting movement, the heavy side of the ring rises up.



This is how the tipped ring spins, with the CM in the rotation axis:



This is the ring without the tip;
it is not very different. 
Again, the CM is pulled away from the spin axis by the centrifugal force, but the ring is spinning about the vertical axis in counterphase, (the TMI_tip is larger than the AMI), so the CM moves towards the spin axis, (green line), instead of getting away from it.

The CM moving towards the spin axis makes the ring to tilt, like when the ring had the tip, but, in this case, since the tip is missing now, the tilting movement becomes a rolling movement. 
As the ring rolls, the contact point changes position, (it didn't change position when there was the tip), and the spin axis moves away from the CM which is trying to reach it.
So the rolling continues.
Only when the CM reaches the spin axis, the rolling ceases.
This happens when the heavy side of the ring reaches the upper part of the ring.

This is the movement of the CM going towards the spin axis.
Only the rolling is shown, not the spinning, to make evident the movement of the CM relatively to the spin axis:   



This is the complete movement, with the ring rolling and spinning at the same time:



(to be continued)

[Iacopo]

The video below is about a real unbalanced ring spinning, rolling and rising.
The movements are the ones previously described, plus there is also some

BACK AND FORTH ROLLING.

The ring doesn't stop rolling immediately, when its heavy side reaches its upper side, but it continues to roll a bit, by inertia, so the heavy side overcames the point where it should stop, then it rolls back. 
A bit like a pendulum, the ring rolls back and forth a few times, with the heavy side trying to reach the upper side of the ring.

Everytime that the ring stops rolling, the ring becomes vertical, like spinning temporarily in sleeping position.
Then the ring starts rolling in the opposite direction.
The faster the ring rolls, the more tilted the position of the ring: this is because, when the ring rolls, its contact point has to travel, tracing a circle in the spinning surface.  The faster it rolls, the larger the circle. The CM instead stays near the spin axis, and this makes the ring to roll in a tilted position.

In the video, for making the observation a bit easier, I point out when the ring is not rolling, and the direction of the rolling.

Last observation: there is some back and forth rolling even in the beginning, before the rise, about the lower part of the ring;
maybe this happens because, in the beginning, the spin speed is higher, and the contact point slips a bit.
If the contact point slips, the leverage for making the ring to roll pivoting on the contact point becomes less effective, and the CM migh "prefer" to move towards the spin axis in the lower part of the ring, by making the tip to slip.
When the speed decreases enough that the slipping doesn't happen anymore, the dynamics becomes the explained one. 

[Iacopo]

CONCLUSIONS:

The thrust that makes the heavy side of an unbalanced spinning ring to rise up, comes from the centrifugal force.
The centrifugal force pulls the center of mass away from the spin axis, but, since the ring is spinning in counterphase, (because the TMI_tip is quite larger than the AMI), the center of mass moves towards the spin axis instead, (like it happens in unbalanced regular spinning tops spinning in counterphase, or in the tipped ring).

The movement of the center of mass towards the spin axis, pivoting on the contact point, makes the ring to roll, and its heavy side to rise.  When the CM reaches the spin axis, the heavy side is in the upper side of the ring.
There is some back and forth rolling, as the CM tries to reach the spin axis.

The rolling causes the ring to spin in a tilted position. Everytime that the ring stops rolling, the ring spins in a vertical position again.

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I observed the tippe top, that in some way is not very different from the spinning ring.
So, in the beginning, I thought that this explanation could help understanding the tippe top too.
But it can be seen that generally tippe tops appear to spin about their CM, not about the contact point, and this is an important difference from the spinning ring.  If the CM stays in the spin axis, there is no leverage for the centrifugal force to make the tippe top to roll, like explained for the unbalanced ring.

So I consider this explanation valid for the unbalanced discs and rings, but not the tippe tops and the eggs.

[ortwin]

Yesterday I went with my family to a spectacular artistic show in town: "Feuerwerk der Turnkunst"


There were nor real spinning tops in the show, nevertheless I was reminded of this thread by the two guys and the "Cyr Wheel" it is apparently called. Best you have a look at this video to know what I am talking about:





Obviously they do not use any formulas and such, but they definitely know what to do to that ring for it to behave in a certain complicated way a few seconds later.

[ta0]

I don't know if/when I will ever have time to revisit this thread , but I would like to.

The Cyr wheel is very appealing to me, but when I have had the opportunity at juggling fests, I had not dared to try it. Perhaps one day.
We discussed it on this thread: Cyr wheel

[Iacopo]

Yesterday I went with my family to a spectacular artistic show in town: "Feuerwerk der Turnkunst"

Yes, spectacular ! They are clever with that wheel !