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Author Topic: The slipping top: two new experiments.  (Read 3432 times)

Iacopo

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Re: The slipping top: two new experiments.
« Reply #30 on: November 04, 2019, 04:52:47 AM »

Although the torque created by rolling friction does not directly produce a horizontal force, it results in a horizontal force due to its braking effect and the inertia of the top.

Apparently this should brake the precession, but now I am not so sure, because, while the tip linear speed decreases, the angular speed of the precession instead increases, since the tip moves along a spiral trajectory nearer and nearer to the center.
What is the real effect of all of this on the rise ? The correct point of view is that of the decreasing linear speed or that of the increasing angular speed ?

Whatever the answer, I believe that this would not change my conclusion about the slipping issue, because both rotational friction and rolling resistance are very weak torques, compared to the force necessary for to cause the slip of the top.

« Last Edit: November 04, 2019, 05:17:36 AM by Iacopo »
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #31 on: November 04, 2019, 12:47:28 PM »

This is the second part of the second experiment:
I spun the top on the tilted, (4°), glass mirror.
I put a sheet of paper on the mirror and I spun the top on it.
Then I removed the paper and I painted the mirror with a thin layer of silicon rubber; when the silicon rubber was hardened, I spun the top on it.

I spun the top with the carbon steel and the teflon ball tip.

The results are surprising, because the top slips especially on the rubber surface.
This should not happen, because rubber is less slippery than glass.

What's going on ?


« Last Edit: November 04, 2019, 12:51:58 PM by Iacopo »
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #32 on: November 04, 2019, 03:49:34 PM »

Observing the silicon rubber surface after the top has spun on it, it is possible to see that the tip of the top has left a slight groove on it.
The groove is not permanent, it tends to disappear by the time.
The width of the groove is about 1/2 mm, so, the diameter of the contact point, presumably, was about of the same measure.

« Last Edit: November 04, 2019, 03:57:07 PM by Iacopo »
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ta0

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Re: The slipping top: two new experiments.
« Reply #33 on: November 04, 2019, 08:42:51 PM »

That it slips more on the rubber surface is in fact surprising.

As it sinks on the rubber, the rolling resistance has to be significantly larger. If is was very large, it could explain the new trajectory, as gravity would have more time to act, but it's not the case here.
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #34 on: November 05, 2019, 02:14:02 AM »

As it sinks on the rubber, the rolling resistance has to be significantly larger.

In fact the top rises rapidly, maybe 5 times faster than it does spinning on glass, (with the carbon steel ball).

Certainly the rolling resistance is high, because the presence of the groove means that the elasticity of the silicon rubber is poor, (a ball made of this rubber doesn't bounce well), the rubber compressed by the tip does not expand back immediately, so the support for the tip is asymmetrical; there is support in front of the tip but not at its back. 
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #35 on: November 05, 2019, 03:35:15 AM »

The drawing below is about the contact point of the top walking on the silicon rubber surface;
the contact point diameter is about 0.5 mm.
The angle of tilting of the spinning surface is 4°, and that of the top is about 1°, so the angle between the top and the spinning surface is about 5°.  The diameter of the ball tip is 4.76 mm, so the distance of the center of the contact point from the spin axis is 0.21 mm;
since the radius of the contact point is 0.25 mm, the spin axis passes through the contact point, (the red dot in the drawing).

The arrows represent the direction of motion of the ball tip surface at the contact point.
There is a chaotic situation, with a lot of forced slipping, since each point of the ball contact area is going in a different direction, with a different speed.   

« Last Edit: November 05, 2019, 03:42:18 AM by Iacopo »
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #36 on: November 05, 2019, 04:15:26 AM »

Let's suppose that this top walks horizontally on the tilted rubber plane, along the no slip direction, (blue arrow).
Since the ball tip is no more in contact with the rubber surface at the back, (because the rubber compressed by the rolling tip does not expand back immediately), the real contact point area is approximately the one pictured below.

But looking at the direction of the arrows in the contact point, it can be seen that the average traction is not directed horizontally, (big red arrow). 

« Last Edit: November 05, 2019, 08:37:43 AM by Iacopo »
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #37 on: November 05, 2019, 04:46:15 AM »

Also, the traction comes mainly from the upper part of the contact point, where the speed of the ball surface is higher.
In the lower part of the contact area the speed is lower, and even reversed below the center of rotation, (the red dot), so this part of the contact area brakes the traction.

For these reasons the traction is not directed horizontally, but obliquely.

The top spinning on the tilted rubber surface goes downhill, (blue arrow), but this is not slipping due to the tilted spinning surface.
It is a particular dynamics due to a large contact point area and poor elasticity of the rubber spinning surface, which makes for an asymmetrical contact point, so that the resultant average traction is directed obliquely. 

« Last Edit: November 05, 2019, 08:23:59 AM by Iacopo »
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #38 on: November 05, 2019, 05:27:52 AM »

The same distorted direction of the traction can be seen when the top precesses on the silicon rubber surface:
note that the top walks towards the outside, or, in other words, that the stem stays very tilted backwards while the top spins:

I checked for backwards slipping, there was 17 % backwards slipping for this top precessing on the silicon rubber surface set horizontally.

https://www.youtube.com/watch?v=LofZ70ibHB0
« Last Edit: November 05, 2019, 08:29:47 AM by Iacopo »
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #39 on: November 05, 2019, 07:07:31 AM »

CONCLUSIONS:

Spinning top slip backwards while precessing, even after the acceleration phase; I don't have many data about this behaviour, but the few times I checked for it, I always found it to be true.  The percentages of backwards slipping I found are 10 % for the top with the carbon steel ball tip spinning on glass, 7 % for the same top but with a teflon ball tip spinning on glass, 15 % for the same top with the carbon steel ball tip spinning on glass but unbalanced, (there was much wobbling), and 17 % for the same top, with the carbon steel ball tip spinning on silicone rubber.

Spinning tops tend to rise in vertical position while they precess.

The backwards slipping and the rising behaviour can make suppose the existence of a resistance of the flywheel, because of the gyroscopic motion, to the precession;  this would constrain the top to slip backwards along the precession trajectory.
At the same time, the tip, acting as a traction wheel, and pushing the top forwards, against this resistance, located at the height of the flywheel, and directed backwards, would introduce a torque to the top, in the direction of making the top to fall backwards.
This torque has the correct direction for making the top to rise, (because of the gyroscopic effect).
So, the gyroscopic motion braking the precession would elegantly explain both the behaviours.

On a theoretical level, I never understood this explanation.
I am not saying that it is necessarily wrong, but I don't understand it. 
I believe that the gyroscopic motion introduces a steering action to spinning tops, (making them precess), but not a braking action.
In whatever way I think to the forces and their directions in play, I can't figure out this braking action.

The first experiment in this thread shows that the magnitude of this supposed braking force, if existent, is lower than the sum of the rotational sliding friction and the rolling resistance at the tip.
Rotational sliding friction was calculated for the top spinning in sleeping position: 7 millionths of Newton meter.
When the top spins in tilted position and precesses, rolling resistance adds to the rotational friction.
Anyway, their sum should not be higher, because rotational friction decreases when the top is tilted, and the appearance of rolling resistance does not compensate for the diminished rotational friction, because rotational friction is a stronger torque.
This can be seen in the videos with the floating dishes: the top precessing on the dish doesn't seem to accelerate the dish forwards more rapidly than when the top is simply in sleeping position on it.
So, the supposed braking force, if existent, should be no more than 7 millionths of Newton meter.

The second experiment shows that the torque necessary for to cause the slipping of the tested top is 0.02-0.04 N, which translates into 200-400 millionths of Newton meter in the case of the last video with the dish.
This is a far too high value, compared to 7 millionths of Newton meter.
Even considering possible errors in the accuracy of my tests, it doesn't seem risky to conclude that the supposed braking force, even if existing, is too weak for to be the cause of the top slipping backwards.
There must be another cause for the slipping.

The last experiment shows that interactions happening in the contact point area can produce apparent slipping.
It is not necessary a push from the outside for to cause an apparent slipping.
Is this the case for the backwards slipping of spinning tops ?  I have no idea, more experiments and more thinking would be needed.
If I will find something interesting, I will post it here.
 

       
« Last Edit: November 05, 2019, 11:58:58 AM by Iacopo »
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ta0

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Re: The slipping top: two new experiments.
« Reply #40 on: November 05, 2019, 10:56:26 AM »

I agree with your explanation about the direction on the rubber coating. When I receive the ball tip adapter that you sent me, I may repeat your experiment.

I need to think about the conclusions from these experiments. Thanks for the food for thought!
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Iacopo

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Re: The slipping top: two new experiments.
« Reply #41 on: November 05, 2019, 03:15:36 PM »

Thanks for the food for thought!

You are welcome ! I too am learning and I have many doubts, these issues are complicated.
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