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Author Topic: The slipping unbalanced top: a riddle and an experiment  (Read 307 times)

ta0

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #15 on: June 28, 2020, 06:42:58 PM »

Jeremy
Imagine the precession is slow enough that you can paint the stem while it stays in one place. If the stem has a round cross-section but is spinning with respect to a point B that is off center, on each revolution the light part will extend outwards more than the heavy side. So if you carefully approach the brush, you will only touch the light side.
Adding the precession will not affect this. The revolution and precession don't have to be in sync as one side of the stem sticks outwards more than the other.
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ta0

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #16 on: June 28, 2020, 09:02:07 PM »

What I said above is strictly valid if the spin axis is through the real center of mass and the unbalance is only apparent with respect to the geometrical shape of the top, so the movement is not really a wobble. If there is real wobbling and the principal axis describes cycloid loops while precessing, this might not be right: if those are bigger than the shift of the center of mass then yes, you would need a synchronicity.
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Iacopo

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #17 on: June 29, 2020, 04:15:30 AM »

Please know that I don't mean to come across as antagonistic when I balk at certain interpretations of the empirical data. Maybe I'm overly careful, but I've seen too many of my own pet theories go down in flames with the arrival of new data or a new journal article. The one lesson I keep learning over and over again: Don't get too attached to any explanation. Tops are way more complicated -- and humbling -- than they look.

I think that nobody here treats these issues as religion, believing this or that by faith, or choosing to belove an explanation for whim, even if we could tend to think this of the others, when they don't agree with what we say.
I think we all here are honest and sincere expressing our own ideas, just our knowledge and way of thinking are not exactly the same and sometimes we reach different explanations.

As we learn, and our knowledge evolves, our ideas can become more accurate, or change, less or more, based on the acquisition of the new concepts.
I feel some of my ideas are stronger, others weaker;  the explanation I gave here for the marks at 90°, I feel it like a weak one.
But it is the only one I have at present.  The discovery that unbalanced tops tilt sideways, (and receive the brush marks sideways), when they spin slipping, lead me to this theory, making me think that the sideways braking force at the tip is linked to the sideways tilt of the top, even if I am not very sure how this braking force should make the stem to tilt in the opposite direction.   
 
« Last Edit: June 29, 2020, 04:19:03 AM by Iacopo »
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Iacopo

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #18 on: June 29, 2020, 05:09:45 AM »

After all, the gravitational torque acting on any real top generally produces precession, not tilt.

In this case the torque produces tilt, not precession.

For the gyroscopic tilt, (with the 90° delay), to happen, the top must spin relatively to the torque, so that each mass point in the flywheel receives a rapid sequence of alternate pushes in the two opposite directions, while spinning.

In the case of unbalance, this doesn't happen.
The added weight is attached to the top so the torque spins together with the top, and the side of the top pulled down by the added weight is always the same.
That side is permanently pulled down by the torque of the added weight;  it is not pulled alternately up and down while spinning as it happens in precession.

In these conditions the gyroscopic tilt with the 90° delay doesn't happen.
The motion happens directly where the force is applied, and the heavy side sinks down.
-----------------------------------------------------------------------------------------

It's the same in my explanation about the sideways marks:

I typed:"It seems like the braking force, pivoting on the CM, makes the stem to tilt towards the opposite side, C, (yellow arrow)."

Even in this case it is not expected the gyroscopic tilt with the 90 degrees delay to happen, because the braking force at the tip spins together with the top, and the side of the top receiving the braking push is always the same.  The torque is directly transferred to the flywheel, which tilts accordingly in that same direction.



« Last Edit: June 29, 2020, 06:35:17 AM by Iacopo »
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Iacopo

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #19 on: June 29, 2020, 06:14:17 AM »

And the marks often end up on the light side (180° phase angle), not the heavy.

This depends on the proportions of the top:

If the unbalanced top is sufficiently large and low, the marks end up always on the heavy side, (unless slipping).

But in unbalanced tops tall and narrow, (I mean, relatively tall and narrow: in the transient proportions the AMI is still larger than the TMI), the marks are always on the light side, (unless slipping).

This is because the tall/narrow tops spin about the CM, like an object spinning in mid air.

Unbalanced large/low tops show to be unable to spin about the CM, (unless slipping).
This is maybe due to the proximity of the CM to the tip and to the centrifugal force which tends to keep the flattened flywheel orthogonal to the rotational axis.
Being nearer to the tip, the top must tilt more for the CM to reach the rotational axis, and the top could refuse to tilt because the flattened flywheel is kept orthogonal to the rotational axis by the centrifugal force.



Centrifugal force wanting to align the top to the rotational axis and opposing the CM wanting to go in the rotational axis.
This can happen only with flattened flywheels, large and low tops.
The torque on the flywheel due to the centrifugal force is not subjected to the gyroscopic tilt + 90° delay, because the torque spins together with the top, and the torque has always the same direction relatively to the top. 

« Last Edit: June 29, 2020, 06:52:12 AM by Iacopo »
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Iacopo

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #20 on: June 30, 2020, 04:47:02 AM »

This is the second top spinning on the glass pane.
It has a HSS tip so there is a stronger braking force relatively to the first tested top, which had a slippery teflon tip.

With the teflon tip the top seemed to rotate about the center of mass, behaving in this sense like an object spinning in mid air, and the little friction at the tip didn't introduce important changes in this behaviour.

With the HSS tip, like in the top with the teflon tip, the rotational axis is shifted towards the added weight, but, almost certainly because of the increased sideways braking force at the tip, there is also a sideways shift of the rotational axis, as shown in the video:

https://www.youtube.com/watch?v=KHO9_sP3TF4


Summary:

When an unbalanced top spins while slipping, the rotational axis (blue x in the drawing), is shifted towards the center of mass.

The tip is dragged on the spinning surface making a circle about the rotational axis.

The braking force at the tip, (red arrow in the drawing below), is towards the left, (top spinning counterclockwise), and the stem tilts towards the opposite direction, the right.

The marks on the stem are about 90 degrees after the heavy side.

With a slippery tip the top seems to spin about the center of mass.
But with a normal tip, like hss, the rotational axis, (blue x), is also pushed sideways, towards the left in the drawing.


« Last Edit: June 30, 2020, 04:53:55 AM by Iacopo »
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Iacopo

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #21 on: Today at 01:51:36 PM »

I made a new experiment.

I expected in the previous experiment the rotational axis to become shifted sideways, because of the sideways braking force at the tip, but not towards that side, the opposite.  I was a bit confused so I made this new experiment.

I made a balanced wooden wheel and mounted it to the lathe through a flexible shaft.
When the lathe is turned on, the wheel spins about its center of mass, which is normal.

Then I added a sheet of plastic to a side of the wheel, which creates a lot of air drag at that side.
I added a screw at the other side of the wheel, to balance it.
In a vacuum system this would still spin balanced and without wobbling, but the sideways asymmetric air drag causes a shift of the rotational axis, in the same way of the sideways asymmetric braking friction of the tip in the top.

I tested the wheel at various speeds and I found that the position of the rotational axis changes with speed.

At about 500 RPM it is not stable, it wobbles a lot.
The most interesting fact is that the rotational axis shift below and above 500 RPM is completely different;

At low speed, less than 500 RPM, the wheel becomes shifted approximately in the same direction of the push of the air drag, which is intuitive, and the rotational axis becomes shifted towards the opposite side obviously.

But over 500 RPM there is a sudden change of behaviour, and the wheel becomes shifted in the opposite direction than the push of the air drag, which is not intuitive.

Here is the position of the rotational axis, (orange dot), depending on speed, (RPM). 



This is the video, which helps understanding what I made:

https://www.youtube.com/watch?v=U0ZD1qSnJNE
« Last Edit: Today at 03:45:28 PM by Iacopo »
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ta0

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #22 on: Today at 02:39:53 PM »

What did you mark with a pencil circle and an arrow?
The drawing showing the positions of the center of rotation is just a little larger than the size of the hole in the middle of the disk, isn't it?

Well, now you are giving Jeremy the go ahead to talk about whirl!  ::)  >:D  ;D ;D
What you describe seems like a resonance at 500 RPM and a 180 degree shift between both sides of the resonance frequency is common. I say this without thinking about the specifics in this case and without having read any whirl papers (not enough time in the day and I'm not very interested) but from resonances in general.

« Last Edit: Today at 02:44:16 PM by ta0 »
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Iacopo

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #23 on: Today at 03:44:08 PM »


Well, now you are giving Jeremy the go ahead to talk about whirl!  ::)  >:D  ;D ;D

You made me smile, Ta0.

What you describe seems like a resonance at 500 RPM and a 180 degree shift between both sides of the resonance frequency is common. I say this without thinking about the specifics in this case and without having read any whirl papers (not enough time in the day and I'm not very interested) but from resonances in general.

I have an idea for a simpler experiment which should help understanding, maybe tomorrow..
I don't think there is whirling here, because there is no vibration. The same like in unbalance wobble, the wobble is apparent, and the disk remains tilted always in the same direction, (at constant speed). 
That direction, intuitively, should be that of the applied force, that of the air drag in this case.
But this happens only at low speed.

The simpler experiment I am thinking about is to use a simple unbalanced wheel, mounted in the lathe through the flexible shaft:

With the experience of the today experiment, I expect that, at low speed, the heavy side becomes pulled outwards, with centrifugal force working in the intuitive way.
At higher speed instead, I expect the behaviour to invert, and the heavy side to be pulled inwards, towards the rotational axis.


Maybe all of this could help understanding something about the slipping tops, like the tippe top.


What did you mark with a pencil circle and an arrow?
The drawing showing the positions of the center of rotation is just a little larger than the size of the hole in the middle of the disk, isn't it?

The circle is the side of the wheel where there is the plasic sheet, and the arrow is the direction of the air drag;
intuitively, the flexible shaft, and the wheel, should remain tilted towards that direction, while spinning;
but this happens only at low speed, (200, 290 and 425 RPM).

Yes, the drawn circle may be larger..  I drew it to contain all the dots and not in scale to the hole.
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ta0

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Re: The slipping unbalanced top: a riddle and an experiment
« Reply #24 on: Today at 06:36:54 PM »

This is definitely whirl.

When you push the axle side wise, it vibrates. I count 25 frames per second on that video and very close to 3 frames per vibration period. So I would expect a resonance at 25/3 = 8.3 Hertz = 500 RPM . . .  :)

This is a diagram of the resonance of a spring pendulum with different levels of damplng (from this lab experiment: http://www.physics.rutgers.edu/~jackph/2005s/PS02.pdf):



The graph on the right shows the difference in phase between the force and displacement and you can see that it's in phase at frequencies below resonance (it moves in the direction of the force) and its at 18o degrees above (it moves in the opposite direction as the force).
« Last Edit: Today at 06:40:29 PM by ta0 »
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