The unbalanced spinning ring; an explanation

[Iacopo]

I am in the bed, with bronchitis, for many days. At some point I felt a bit better and I started working at my new tops, but in the evening I had fever again. This is an annoying bronchitis, quite persistent.

The only good thing about all this forced rest is that I have so many hours for thinking. I started to think about the tippe top; the tippe top is a real mistery, it seems impossible to find a simple and convincing intuitive explanation of its behaviour.  There are other objects that behave similarly to the tippe top, like eggs, unbalanced discs and rings... their heavy side rises while spinning. But what is the reason of the rise ?
 
I thought that maybe the unbalanced discs and rings are easier to understand, because they are flattened, and could be considered like two-dimensional, which could make the reasoning easier.
So I thought about them, until I had a realization. Maybe I found why these objects rise while spinning.
I thought to the new idea, to the details, and I didn't find any errors in it.  So much that I decided to start this thread.

This is about the unbalanced spinning rings and discs, but I believe that the same concepts are suitable for to explain the spinning egg and the tippe top behaviour. It will take some days for to explain everything, (not that there is a lot to say, at the countrary, the theory is quite simple, but I would want to make a few videos for to show some things and I am still a bit too weak now).
   

[Iacopo]

This is an old video by Veritasium, where he shows the behaviour of an unbalanced disc. Even if the title is "Spinning disk trick solution", there isn't a real explanation in the video:

https://www.youtube.com/watch?v=tDr26U49_VA

[Iacopo]

These are two attempts to explain the unbalanced disc and the tippe top behaviour:

https://www.youtube.com/watch?v=Kwihc4kbNVA


https://www.youtube.com/watch?v=pwl-rBVbWAY


They both say that the torque due to the friction at the contact point is directly responsible for the rise;
both these explanations seem wrong to me.

In the first video, the showed torque has not the correct direction for causing the rise of the tippe top: this is especially evident when the tippe top spins with its stem horizontal.

In the second video, it is supposed that a gyroscopic effect deviates that same torque in the correct direction for the rise.
There are two problems with that explanation:
first of all, for to have a gyroscopic effect, the object must spin relatively to the torque causing it. But this is not the case, because the direction of the friction at the contact point, (and that of the consequent torque), spins together with the object, and is steady relatively to it, (video below).  In these conditions there cannot be gyroscopic effect: 

https://www.youtube.com/watch?v=wdW4BvVol_s

But, even if there was gyroscopic effect, it couldn't work anyway.
Replicating the reasoning of the second video, in the pic below, there is a ring, spinning clockwise, about the center of mass, (the green line is the rotation axis);
The contact point is dragged in circular motion and the friction would cause the ring to tend to tilt, (orange arrow).
If there was gyroscopic effect, this tilting force would become tilting movement 90 degrees later, (blue arrow).
This would make the heavy side of the ring to sink down, not to rise up. There is some confusion, about the directions, which led to wrong conclusions, in that video.
So this is not the correct explanation, either.
   

[ta0]

I hope you feel completely well soon, Iacopo.

I agree with you, the first explanation to me is wrong and in the second the precession effect of the friction is in the wrong direction and would sink the weight.

I look forward to your explanation (although I'm pretty busy right now with the ITSA general assembly and the worlds in Tokyo coming up).

[Iacopo]

I hope you feel completely well soon, Iacopo.

Thank you, Jorge. 

Before to go on, a clarification about the gyroscopic effect:
when I say that there is not gyroscopic effect, I mean so just relatively to that particular situation described in the "Basic saucer physics" video. 

Which doesn't mean that there is no gyroscopic effect at all, in spinning discs and rings.  If the spin axis is not perfectly vertical, these spinning things do precess, (video below), like normal spinning tops. The torque due to gravity trying to topple the disc/ring in this case is obviously subjected to the gyroscopic effect. 

https://www.youtube.com/watch?v=lq-_bfr_zQ8

[Iacopo]

Centrifugal force is at the core of my explanation.
The effects of centrifugal force are not so obvious, like it can be seen in this video:

https://youtu.be/bCpnw822P2s

Sometimes the spinning mass, under its effects, is pushed outwards from the rotation axis, which is the simpler and more intuitive situation:



Other times, the spinning mass seems like to be attracted towards the rotation axis. 
Maybe it could be said that the ball now is spinning in counterphase relatively to the centrifugal force, there is a 180 degrees delay, so the ball is pushed inwards, towards the rotation axis, instead of outwards, far from it.
Maybe, it could be just said that the ball is trying to spin about its center of mass.
It is interesting to note that the stick holding the ball, (photo below), is now bended inwards, making visually evident the force that attracts the ball towards the rotation axis.EDIT ... making visually evident the apparent reversal of the direction of the centrifugal force.
I believe that this is the way how discs, rings, eggs and tippe tops spin: their centers of mass are attracted towards the rotation axes, while they spin.



Another observation: Veritasium said that he felt that his wooden disc was not slipping during the rise, and I agree with his observation.
So I made a new animation, this time placing the rotation axis, (the green line), through the contact point;
the center of mass is the red dot.

Look at the animation, and think: the ring spins without slipping and the center of mass is attracted towards the rotation axis.
What do you think that it will happen ?
Maybe at this point you can start to figure out where I am going with this...

https://youtu.be/qZ88pyx6Jrg

[Iacopo]

The center of mass, (red dot), tends to go towards the rotation axis, (green line).
But the ring doesn't slip at the contact point, so the movement can only happen in the upper part of the ring, pivoting on the contact point, (blue arrows);
this makes the ring to roll, and the heavy side of the ring to rise up.   



As soon as the ring rolls, the contact point shifts along the circunference, and the same dynamics repeats, until the heavy side of the ring reaches its upper side; at that point the center of mass has reached the rotation axis, the torque causing the ring to roll ceases, and the ring spins balanced and smoothly, with its heavy side on the top.

If the spinning surface is very slippery, the unbalanced ring cannot rise: the reason is that, if the contact point slips, the ring spins about the center of mass since from the beginning of the spin, and not about the contact point, which is dragged in circular motion about the rotation axis. The center of mass stays always in the rotation axis. The center of mass cannot be attracted towards the rotation axis because it's already there. This prevents the torque which would cause the ring to roll and its heavy side to rise up.   

[ta0]

Other times, the spinning mass seems like to be attracted towards the rotation axis. 
Maybe it could be said that the ball now is spinning in counterphase relatively to the centrifugal force, there is a 180 degrees delay, so the ball is pushed inwards, towards the rotation axis, instead of outwards, far from it.
Maybe, it could be just said that the ball is trying to spin about its center of mass.
It is interesting to note that the stick holding the ball, (photo below), is now bended inwards, making visually evident the force that attracts the ball towards the rotation axis.
I believe that this is the way how discs, rings, eggs and tippe tops spin: their centers of mass are attracted towards the rotation axes, while they spin.

I don't think this is how it works. You are right that there is a 180 degree phase delay between the force at the drill end of the stick and at the ball end. But this is due the vibration of the system composed by the flexible stick and the mass at the end. The centrifugal force is always pushing the top to the outside. This cannot explain why a rigid top would rise.

[ortwin]

If I throw a boomerang and land the top on my hand, often a circular motion of that hand is needed to get the top to spin upright on the palm.


If I throw a bearing top to spin on the ground, it will usually not rise of of it lands at an angle.


If I throw a fixed tip top to spin to the ground, it will precess while tilted.  The tip usually describes a circle. If it is fast enough, the top rises. The direction of the torque caused by the friction due to the circular motion of the tip corresponds to the torque excreted by the hand in the boomerang case.
Does this help at all? I "believe" in the friction as cause for the effect we see in tippe tops.

[ta0]

Does this help at all? I "believe" in the friction as cause for the effect we see in tippe tops.

There is no doubt that without friction the tippe top doesn't rise. It can be easily demonstrated experimentally.

If I throw a fixed tip top to spin to the ground, it will precess while tilted.  The tip usually describes a circle. If it is fast enough, the top rises. The direction of the torque caused by the friction due to the circular motion of the tip corresponds to the torque excreted by the hand in the boomerang case.

Yes, but there is no clear relation with the case of a tippe top.

[Iacopo]

If I throw a fixed tip top to spin to the ground, it will precess while tilted.  The tip usually describes a circle. If it is fast enough, the top rises.

It seems to me that we are talking about different things.
You are saying about normal spinning tops, that precess with their spin axes in tilted position, and the rise is about the spin axes, that become vertical, after some time spinning.
I am saying about unbalanced rings and discs, eggs and tippe tops, which spin with their spin axes always in approximately vertical position; the rise in these cases is not about the spin axes, but the heavy side of these spinning objects, which, "slipping" through the spin axis, (which does not change orientation), tends to go in their upper part, while spinning.
I believe that the causes of the two behaviours are not the same. 

[Iacopo]

The centrifugal force is always pushing the top to the outside.

You are right, centrifugal force is always directed outwards.
Even in the spinning ball sample.
My expression "mass attracted towards the spin axis" was not good, so I feel the need to describe better what I think it happens;

When the ball spins, the centrifugal force bends the stick towards the outside, (the intuitive situation, drawing in the middle).
But if the drill turns too fast, it may happen that the "precession" can't take the pace of the "rotation", and a lag develops: the ball is still at the left when the drill turns for another 180 degrees, and as a result the stick becomes bended inwards, (drawing at the right), then, for some reason, the ball continues spinning staying balanced in that way. 



So it is not correct to say that the center of mass is attracted by the rotation axis, anyway the practical result is that the stick becomes bended inwards, which seems what it matters to me.
We already discussed about this sort of issues in the thread about resonance and phase shift.  The experiments showed that spinning tops can spin in phase and in counterphase too. Why the same shouldn't happen with tippe tops and similar items ?   

[Iacopo]

This is the final part of my reasoning, which was not completed yet.

When the ring starts rolling, it can't spin staying always in the same spot of the ground, it walks.
As the ring rolls/walks while spinning, its contact point traces a circular trajectory on the ground, and, because of this, the ring spins in a tilted position. The more rapid the rolling relatively to the spin, the more tilted the ring moves during the rise.

The consequential logic of the movements is:
1- The center of mass goes towards the spin axis.
2- As a consequence, the ring rolls, and its heavy side rises up.
3- The rolling causes the ring to walk, the contact point traces a circle on the ground, the ring has to spin in tilted position.

This is how it looks, in slow motion:

https://youtu.be/QV2bgFiVM2s

[ortwin]

You say:

If I throw a fixed tip top to spin to the ground, it will precess while tilted.  The tip usually describes a circle. If it is fast enough, the top rises.

It seems to me that we are talking about different things.
You are saying about normal spinning tops, that precess with their spin axes in tilted position, and the rise is about the spin axes, that become vertical, after some time spinning.
I am saying about unbalanced rings and discs, eggs and tippe tops, which spin with their spin axes always in approximately vertical position; the rise in these cases is not about the spin axes, but the heavy side of these spinning objects, which, "slipping" through the spin axis, (which does not change orientation), tends to go in their upper part, while spinning.
I believe that the causes of the two behaviours are not the same. 

Hmmm, actually I like to think that it is the same thing we are talking about. A regular throw top, a tippe top, an unbalanced ring, euler's disk ... should all be just special cases of a general top following the same laws.
Well, that much is easy to say, I admit finding good analogies and explanations is quite another thing. I hope I can come up with something more useful in future.

[Iacopo]

Hmmm, actually I like to think that it is the same thing we are talking about. A regular throw top, a tippe top, an unbalanced ring, euler's disk ... should all be just special cases of a general top following the same laws.

To call them "different things" or "special cases" is a bit philosophical... the explanations might have to be different, in the different "special cases".

The explanation I am giving here is not suitable for normal spinning tops, because the center of mass wanting to move towards the spin axis, which can produce a thrust in the case of the ring, can't do that in the case of the normal spinning top, because the center of mass is already in the spin axis, in a normal and balanced top, even if the top is spinning in a tilted position.