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Author Topic: The reason that spinning tops rise  (Read 2373 times)

Iacopo

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Re: The reason that spinning tops rise
« Reply #15 on: July 16, 2018, 11:52:22 AM »

THE EFFECT OF THE SLOWING DOWN OF THE SPIN SPEED, (DUE TO AIR DRAG AND TIP FRICTIONS),
ON THE RISING OF THE TOP

When a top spins and precesses, like in the drawing below, the linear velocity of the top axis, (green line), along the precession trajectory, at the level of the tip, is higher than the linear velocity of the center of mass, (it traces a larger circle with the same angular speed).

In absence of frictions, the two linear velocities would be constant.
In this situation there would be no torque and the top would not rise nor fall.
The tip going faster than the center of mass, (as for linear speed), does not create a torque on the top axis;
an acceleration is needed for to create a torque.



Which is the case of real tops, their velocities are not constant.
Because of air drag and tip frictions, tops slow down while spinning.
The diminishing spin speed of the top causes a braking action at the contact point, so that the linear velocity of the tip along the precession trajectory is coinstrained to diminish, (if the tips doesn't slip, which is the most common case).

While the tip slows down along the precession trajectory, the center of mass would want to continue to go on with its constant linear speed, (inertial speed).

So a torque comes out from this situation.



This torque is in the direction to make the top to tilt more, not to rise.

So, the top slowing down works against the top to rise.
Air drag works against the top to rise.
Rotational sliding friction works against the top to rise too, by both the mechanisms explained, the one of this comment and the one explained in the video.
Rolling resistance is the only mechanism that makes the top rise, as explained in the video, but one effect of rolling resistance is to slow the spin speed of the top, and, in this sense, it fights against the top to rise.

Since real tops do rise if their spin speed is high enough, it can be supposed that the rising torque of the rolling resistance alone is stronger than all the other opposing torques together.
« Last Edit: July 17, 2018, 02:55:29 PM by Iacopo »
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ta0

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Re: The reason that spinning tops rise
« Reply #16 on: July 17, 2018, 01:56:12 PM »

A lot of work and thinking went into that video explanation, Iacopo! Congratulations!

I have not commented yet, because I need to think more about it (and also read that paper that was mentioned above).

Jeremy, do you know if those who disagree about rolling resistance as the cause of the rising top, think the same as Perry, that the cause is the peg that, rolling on the table, " wants to roll the top faster than the precession lets it roll, so that it hurries on the precession, and therefore the top rises" ?  Is this the common given explanation by them ?
Yes, this is the standard explanation (Crabtree, etc.)

Your experience is with your low and heavy rimmed tops, while mine is mainly with throw tops. I will say that in mine the top rises and sleeps before reaching a stable rolling precession. The tip will be accelerating the precession during the rise (I think both sliding and rolling). So, I think Perry's explanation is correct for them, at least.
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Mermouy

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Re: The reason that spinning tops rise
« Reply #17 on: July 18, 2018, 04:56:38 AM »

As usual your video is awesome and soooo interresting!
I will create a special "technical & theorical" page on spintricks as sonn I have time, (this will be an almost lacopo videos only page btw ???)
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Iacopo

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Re: The reason that spinning tops rise
« Reply #18 on: July 18, 2018, 05:05:32 AM »

Yes, this is the standard explanation (Crabtree, etc.)

Thank you, Ta0.  Yes, I remember the explanation given by Crabtree is similar to that of Perry, but I didn't know about the others.

Your experience is with your low and heavy rimmed tops, while mine is mainly with throw tops. I will say that in mine the top rises and sleeps before reaching a stable rolling precession.

If the tip is slipping while rolling, it could mean that the tip is still accelerating the top along the precession trajectory;
in this condition, there is indeed a resistance, (inertial), of the center of mass to the push of the tip,  and actually this would cause a rising torque.

In the sample I showed in my video the acceleration phase is very brief because I used a wax spinning surface which provides high grip for the tip, but on more slippery surfaces, and especially when the top is started at higher RPM, like in the case of throw tops, the slipping/acceleration phase could last for more time. It is more than plausible to me that during this phase the top would rise above all for the reasons explained by Perry.

But I don't think very much that this is exactly what Perry intended;
he didn't talk about a slipping/acceleration phase, and it seems more like he intended the rules he explained to be valid in all cases, even with a stable rolling precession, without any slipping.

I believe Perry understood correctly great part of the process, he understood correctly the direction of the torque needed for the top to rise, he understood correctly that the processes between the contact points had to be responsible for this torque.
Then, maybe, at that time, the direction of the forces involved in rolling resistance was not known, (it is not very intuitive), so he couldn't find a better explanation than that he gave.
   
« Last Edit: July 18, 2018, 09:06:27 AM by Iacopo »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #19 on: July 18, 2018, 09:23:56 AM »

As usual your video is awesome and soooo interresting!
I will create a special "technical & theorical" page on spintricks as sonn I have time, (this will be an almost lacopo videos only page btw ???)

Thank you, Mermouy, I doubt I deserve an almost Iacopo videos only page as for "technical and theorical", but I'm glad you appreciated the video.
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ta0

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Re: The reason that spinning tops rise
« Reply #20 on: July 21, 2018, 09:44:08 AM »

I read the paper by Cross. Very interesting. It's a perspective I had not seen and along the lines of the explanation you provide on the video.
He mentions two papers about rolling friction which I have not read (and I'm not very eager to read  ::) ), so I guess his explanation of rolling resistance is correct. But my intuitive understanding of rolling resistance was different: I imagined that it came from the "sticking" of the surfaces, so it produced a downwards force behind the center of the wheel, not an upwards force in front. Anyway, either would produce the same torque. However, given the very small lever arm distance to the center, it's surprising to me that such force would cause the rising of the top.
On the other hand, it seems to me that a rolling "reaction" could explain the rise. Because the center of the top is rising, in principle there is an inertia and acceleration the rolling can act against. Because of the rotational inertia of the top, it pushes forward the tip by rolling on the surface, so the total rolling force is forward, even if there is rolling friction in the opposite direction. In which case the classical explanation of "speeding up precession" would still be valid for rolling tips.
The above was my intuitive representation, but it may well wrong.
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Iacopo

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Re: The reason that spinning tops rise
« Reply #21 on: July 22, 2018, 02:00:49 PM »

I read the paper by Cross...
He mentions two papers about rolling friction which I have not read (and I'm not very eager to read  ::) ).

Neither did I. Often these papers are too much complicated for an uneducated person like me. I learned the correct direction of the forces involved in rolling resistance from Wikipedia, it was eye opening to me because I realized soon that this could cause a rising torque.  The only other rising torque I found is that of air drag opposing the precession movement of the top, but this seems usually very week, and also distorted by the Magnus effect, perhaps it could have some influence only in tops walking rapidly along the spinning surface, because of a large radius of curvature of the tip.     

But my intuitive understanding of rolling resistance was different: I imagined that it came from the "sticking" of the surfaces, so it produced a downwards force behind the center of the wheel, not an upwards force in front. Anyway, either would produce the same torque.

I have read that there can be "sticking" too in the rolling resistance dynamics. But the most common cause seems the release phase not so complete and/or not so fast as the compression phase.

However, given the very small lever arm distance to the center, it's surprising to me that such force would cause the rising of the top.

I too was a bit surprised, for the same reason. Especially for more rigid materials like glass, ruby, steel.
The ball top rolling uphill, with the contact point shifted forward by about 1 mm, rises in about half a second.
So it seems like a microscopic shift could be enough for a top to rise in minutes.
I will think if I can make an experiment to understand better this aspect. 

On the other hand, it seems to me that a rolling "reaction" could explain the rise. Because the center of the top is rising, in principle there is an inertia and acceleration the rolling can act against. Because of the rotational inertia of the top, it pushes forward the tip by rolling on the surface, so the total rolling force is forward, even if there is rolling friction in the opposite direction. In which case the classical explanation of "speeding up precession" would still be valid for rolling tips.

I am still reasoning about it..
« Last Edit: July 22, 2018, 03:25:18 PM by Iacopo »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #22 on: July 04, 2019, 11:52:32 AM »

Some months ago I had a long discussion with a student of physics;
he really didn't believe that rolling resistance could be the cause of the rising top,
rolling resistance is certainly far too weak, he affirmed.

I remembered that Ta0 and Jeremy too were doubtful, also for this same reason.

My belief on rolling resistance being the main cause of the rising top is based on
my observation that the torque of rolling resistance is in the correct direction to make a top rise,
then, I don't see any other important possible causes, so I believe that that one must be the main cause.

That student was unhappy with my explanation.  I didn't hear from him anymore.
But I started wondering whether it could be possible to study the issue with numbers;

and I found a way to measure rolling resistance of the balls I use in my tops.
Then I found a way to calculate the magnitude of the rising torque: knowing the data of a top, and the velocity of its rising,
I can calculate the magnitude of its rising torque.

The rising torque of a top, having the same magnitude of the rolling resistance at its tip, would be a clue that rolling resistance is
indeed the cause of the rising.

At this point it was just a matter to make the tests, collect the data, (with different tops and tips), and compare them.

This is what I started to do. 
 
But after some months I am far from definitive conclusions.
These tests, and thinking, take me much time. 
Unfortunately, I don't have much free time.

One day, maybe, I will reach a better understanding of this issue.
In the meanwhile, I would like to share with you very synthetically what I found.


I made two different tests for to measure/calculate the rolling resistance of the balls;
the balls were loaded to simulate the weight of the top on them.
If someone is interested I can explain tests and calculations.
-------------------------------------------------------------------------------------------

ROLLING RESISTANCE measured in millionths of Newton meter:

                                         Test 1            Test 2                             Test 2
                                                        speed 10 mm/sec           speed 70 mm/sec

3/16" TEFLON BALL            34.4                                                         29.9

3/16" RUBY BALL                 3.0                   1.3                                  2.6
-------------------------------------------------------------------------------------------
It is evident that the rolling resistance of the teflon ball is much higher, (ten times and more),
than that of the ruby ball.  I tried also ceramic and carbon steel balls, they have similar values to that
of the ruby ball.  The ruby ball rolling resistance resulted speed dependent. 
The teflon ball rolling resistance instead does not seem speed dependent, but I need more testing to be sure.


Then I calculated the necessary torque, (I can explain how I did), to make my top Nr. 25 to rise at the observed rising speed,
using as tips the same balls of the test above:

------------------------------------------------------------------------------------------------------------------
RISING TORQUE of TOP Nr. 25, (millionths of Newton Meter):

BALL                              Linear speed at the tip        Spin speed       Angle of tilting        Rising torque

3/16" TEFLON BALL              13 mm/sec                    729 RPM                 4.6°                       37.0

3/16" TEFLON BALL              40 mm/sec                   2164 RPM                 5.7°                       37.0

3/16" RUBY BALL                 16 mm/sec                    693 RPM                  6.1°                        3.2

3/16" RUBY BALL                 72 mm/sec                    2179 RPM                7.8°                         8.5
--------------------------------------------------------------------------------------------------------------------

The measured rolling resistance of the teflon ball, (average 32.2), is a bit low relatively to the
found rising torque, (37.0);  the difference is 15 %. 
I don't know if this is due to errors in measurements and/or errors in calculations.
Anyway this result seems to confirm that rolling resistance is at least the main cause of the rising top.

But with the ruby tip the difference becomes more important.
Especially at the higher speed, the measured rolling resistance of the ruby tip, is only 1/3 of the found rising torque.
At present I can't imagine the reason of this difference.

At a certain moment I supposed that there could be another torque, helping that of the rolling resistance, to make the top to rise faster.
But the only other torque I know that works in the correct direction to make the top rise is that of the air drag opposing the precession movement, (not the main one which opposes the spin movement):

this air drag, intuitively, seemed to me too weak and unimportant, but, for the sake of clarity, I made a test to measure it.
I found that, my top Nr. 25, used in the tests, has about 0.1 millionths Newton meter of this air drag when the linear speed of the top along the spinning surface is 100 mm/sec.  This is practically an irrelevant value.
Air drag really seems not to be the cause.

One thing to consider is that in my rolling resistance tests the balls roll with their axes of rotation in horizontal position, in the top instead the spin axis is tilted, so the conditions of the rolling are in some way different.
Maybe this could explain the differences ?  When I will have time I will test something about this.
Also I should make a top with a higher flywheel so I could tilt it more than I could with the one I used in these tests.
« Last Edit: July 04, 2019, 11:58:52 AM by Iacopo »
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Jeremy McCreary

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Re: The reason that spinning tops rise
« Reply #23 on: July 08, 2019, 02:08:43 PM »

Strong experimental work as usual, Iacopo! Hope to have the time (and battery) to re-digest this entire thread on the airplane today.
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Iacopo

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Re: The reason that spinning tops rise
« Reply #24 on: July 08, 2019, 04:13:50 PM »

Strong experimental work as usual, Iacopo! Hope to have the time (and battery) to re-digest this entire thread on the airplane today.

I too would need more time and battery for these things !  I love to think to the physics of the spinning top but it's time and energy demanding.

By the time I have become more and more convinced that rolling resistance is linked to the rising of the top, I saw this more times, in different experiments.  Whenever there is an increase of the rolling resistance, there is a faster rising of the top.

In one of these experiments I used a particular kind of gyroscope, spun like a spinning top;
this gyroscope allowed me to observe the effects of an increase/decrease of the rolling resistance separately from the effects of an increase/decrease of the rotational sliding friction. 
In normal spinning tops this is not possible, because the rolling resistance and the rotational sliding friction happen in the same point, the contact point of the tip, so if you change the spinning conditions of a spinning top, (spin speed, angle of tilting, kind of tip and of spinning surface), and observe the rising speed, there is no way to understand if the changes of the rising speed are due to the rolling resistance and/or the sliding friction.
The gyroscope I used allows to increase/decrease the rolling resistance leaving unchanged the magnitude of the sliding friction, so that it is possible to observe in which way the rolling resistance affects the rising speed, without being confused by the sliding friction changing together with the rolling resistance.
Then it is possible to increase/decrease the rotational sliding friction leaving unchanges the magnitude of the rolling resistance, so to see the effects of the rotational sliding friction on the rising speed.

I have made a video, (months ago), about it, which I believe it wouild be interesting.
I should put subtitles and some drawings, and post it, (when I have time).

The result of the test with the gyroscope is that an increase of the rolling resistance increases the rising speed,
or, it decreases the sinking down speed, if the gyro is sinking down and not rising. 
An increase of the rotational sliding friction instead, increases the sinking down speed of the gyro, or, it decreases the rising speed, if the gyro is rising.

 
Breafly, I am sure that the rolling resistance is linked to the rising of the top.
What I am not sure, is whether there is another cause too, or not, helping rolling resistance to make the top to rise faster.
Because, from my tests with numbers, it seems that rolling resistance alone is a bit weak to explain the rising speed I observed in the tested top.  It could be that there have been errors in the measurements/calculations, or maybe there were no important errors and in this case there should be another cause, together with rolling resistance, which helps the rising of the top.       
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Jeremy McCreary

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Re: The reason that spinning tops rise
« Reply #25 on: July 08, 2019, 05:54:03 PM »

This is complicated stuff, but my instincts tell me that rolling resistance is at least as important as simple sliding friction -- not only WRT to self-righting, but also perhaps WRT the tip-related component of spin decay during precession.

In spinning tops, we're usually dealing with 2 hard, smooth surfaces in direct contact -- one more or less spherical before contact, and the other flat. In such cases, rolling resistance is largely a matter of elastic contact deformation, and here we enter the engineering realm of Hertzian contact mechanics...

https://en.m.wikipedia.org/wiki/Contact_mechanics

Since other contact processes might also be involved in self-righting and spin decay, I've abandoned "tip friction" in favor of the more inclusive and less misleading "tip resistance".

In vehicular dynamics, a "resistance" (e.g., air or water resistance) is usually a net braking force acting in a direction opposite the heading. In a sleeping top with no tip travel, air and tip resistances would be pure braking torques about the spin axis. With tip travel, you'd have contact forces opposing travel as well.

I'm getting a headache!
« Last Edit: July 09, 2019, 06:59:19 AM by Jeremy McCreary »
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Iacopo

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Re: The reason that spinning tops rise
« Reply #26 on: July 09, 2019, 04:21:16 PM »

This is complicated stuff, but my instincts tell me that rolling resistance is at least as important as simple sliding friction -- not only WRT to self-righting, but also perhaps WRT the tip-related component of spin decay during precession.

The contribute of the rotational sliding friction at the tip is that to push the top in the direction to fall, not to rise.
So its effect on the rise of the top is opposite to that of rolling resistance.
You have a faster rising when you increase the rolling resistance and/or decrease the rotational sliding friction at the tip.

I agree that they also both contribute to slow down the spin speed of the top.

In spinning tops, we're usually dealing with 2 hard, smooth surfaces in direct contact -- one more or less spherical before contact, and the other flat. In such cases, rolling resistance is largely a matter of elastic contact deformation, and here we enter the engineering realm of Hertzian contact mechanics...

https://en.m.wikipedia.org/wiki/Contact_mechanics

I tend to believe that the elastic contact deformations can explain largely the rolling resistance of the teflon balls, which are relatively soft and with slow/poor resiliance, (they bounce little).
But the rigid balls, (like ruby, ceramic, carbon steel..), which have much better elasticity, (they bounce well), and very little deformation at the contact point, (so a very short leverage for to cause rolling resistance), seem to have also some other cause for their rolling resistance.  The article you posted mentions adhesion forces at the contact point, maybe in the case of rigid balls the adhesion forces are an important cause of their rolling resistance.
   
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Jeremy McCreary

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Re: The reason that spinning tops rise
« Reply #27 on: July 13, 2019, 05:39:42 AM »

The article you posted mentions adhesion forces at the contact point, maybe in the case of rigid balls the adhesion forces are an important cause of their rolling resistance.

Agree, adhesion could well be a player with some tip-support combos.

Better article...
https://en.m.wikipedia.org/wiki/Frictional_contact_mechanics
« Last Edit: July 15, 2019, 03:48:05 AM by Jeremy McCreary »
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