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Author Topic: Three experiments with gyroscopes  (Read 3396 times)

Iacopo

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Three experiments with gyroscopes
« on: September 08, 2019, 10:07:23 AM »


In this video, I used gyroscopes for some experiments, with the aim to clarify/confirm some ideas I have about spinning tops.
Sometimes gyroscopes are more suitable than spinning tops themselves, for to understand spinning tops.
Everything is explained in the video.


 https://www.youtube.com/watch?v=s-wt6m7KDFo
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #1 on: September 10, 2019, 08:50:01 AM »

There is a test I made which I didn't include in the video, I explain it here:

I was curious to see whether the weight added on the side of the gimbal of the gyroscope contributed or facilitated in any way to make that side to go down:  in the video it is shown that it is only the friction of the bearings in the base of the gyroscope that makes the weighed down side of the gimbal to go down.

When the torque coming from the friction of those bearings is eliminated, the gimbal stays level and doesn't tilt anymore, while the gyroscope precesses, in spite of the added weight on one side of it.

I wondered whether, from this neutral behaviour, applying torques to accelerate or decelerate the precession, the weight on the side of the gimbal helps in any way that side to go down.

I added 1.2 grams weight to the thread, (see video), so to have a net torque along the vertical axis of the gyroscope 0.000051 Newton meters, in the direction to accelerate the precession.  This made the gimbal to tilt up by 20-22 degrees after 7 precession revolutions.
By saying "the gimbal to tilt up" I mean the side of the gimbal with the added weight to rise.

Then I removed 2.4 grams from the thread, so to have a net torque along the vertical axis of the gyroscope of the same magnitude but with opposite direction, (braking the precession). 
This made the gimbal to tilt down by 20-22 degrees after 7 precession revolutions

The weight on the gimbal, (12.2 grams), didn't influence in any way the tilting speed of that gimbal.
It didn't help the gimbal to tilt down faster, and it didn't brake the gimbal from rising, absolutely.

I made this test because I wasn't totally sure about the result.



   
« Last Edit: September 10, 2019, 08:52:50 AM by Iacopo »
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ta0

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Re: Three experiments with gyroscopes
« Reply #2 on: September 11, 2019, 06:19:55 AM »

Wow, Iacopo, you don't stop to impress me!  :o
The physical simulation of a frictionless precession is genius.
Your whole setup and the video documenting it are perfect. 8)

I have to confess that I'm still not convinced that rolling resistance is the correct explanation but it's not something I can discuss writing on my phone. When I'm back home and have some time, I'll write my thoughts.

Thanks for documenting and sharing your superb experiments!
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #3 on: September 11, 2019, 12:12:23 PM »

Thank you for your kind words, Ta0.

When I'm back home and have some time, I'll write my thoughts.

I will read them with interest.
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Jeremy McCreary

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Re: Three experiments with gyroscopes
« Reply #4 on: September 11, 2019, 01:13:02 PM »

Great experimental work, as always! Still processing your methods and findings. Like ta0, travelling now and can't do it justice on my phone.
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #5 on: September 11, 2019, 02:35:54 PM »

Thank you, Jeremy.  I would like to know your opinion too.
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ta0

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Re: Three experiments with gyroscopes
« Reply #6 on: September 23, 2019, 11:47:44 PM »

On the video you demonstrate that sliding friction force on a non-rotating tip will make the gyro tilt more. That is true. But on a rotating tip (where the tip is rotating faster than it would be by rolling without slip) the sliding friction force will be in the opposite direction! The ball tip pushes the top forward in its precession, and that's the conventional explanation of why a top sleeps. My guess without calculating is that this would be a much bigger effect than that of rolling resistance. But you might be right in that it contributes to the rise (and it's something probably nobody has considered before).

What I don't understand, is why a teflon (PTFE) tip would make the top rise much faster than a steel tip. Supposedly, the friction coefficient of PTFE against steel is about 10 times smaller than between steel and steel (link).  :-\
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #7 on: September 24, 2019, 03:32:56 AM »

What I don't understand, is why a teflon (PTFE) tip would make the top rise much faster than a steel tip. Supposedly, the friction coefficient of PTFE against steel is about 10 times smaller than between steel and steel (link).  :-\

Yes, the sliding friction coefficient of teflon is much smaller, but it can be seen that the top with the teflon tip will not spin longer, in spite of this.  I believe that the reason is that teflon, being a relatively soft material, flattens a bit at the contact point, so there is a quite larger contact point area with it, that should increase the friction.  There is also some wear out of the teflon tip, while the top spins.
In the whole, the rotational sliding friction in a top, with a teflon ball tip or with a carbon steel ball tip, seems similar.
The spin decay is similar.

Anyway I am not sure that sliding friction could make the top to rise.
It seems that you are trying to link the fast rise of the top with the teflon tip to the Perry explanation, but it seems to me that it doesn't work in that way, and that the rolling resistance explanation seems more plausible.

 
But on a rotating tip (where the tip is rotating faster than it would be by rolling without slip) the sliding friction force will be in the opposite direction!

Are you sure that there is slipping of the tip ?
Has this ever been observed, or it is just a theoretical deduction ?
I too read similar statements, but I am doubtful.  I don't have the sensation that the tip slips, while the top spins, nearly always.
Do you know whether this was empirically demonstrated and documented ?
« Last Edit: September 24, 2019, 08:46:59 AM by Iacopo »
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ta0

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Re: Three experiments with gyroscopes
« Reply #8 on: September 24, 2019, 01:07:36 PM »

Are you sure that there is slipping of the tip ?
Has this ever been observed, or it is just a theoretical deduction ?
I too read similar statements, but I am doubtful.  I don't have the sensation that the tip slips, while the top spins, nearly always.
Do you know whether this was empirically demonstrated and documented ?

For a top leaning significantly and making a clear circular path on a flat surface, it's easy to determine by calculating the rolling condition (zero speed for the point of the sphere touching the surface).

If the tilt angle is alpha and the top is spinning at an angular velocity w and precessing at u, the pure rolling condition is:

w sin(alpha) r = u R

where the radius of the circle described by the precession is R and the radius of the tip r.

If the left side is bigger, then the tip is slipping while pushing the top forward. If the right side is bigger, the slipping friction is stopping the precession.

I always assumed the first case was generally true, but a back of the envelope calculation for one of my tops gave me that it's not so obvious  :-\
« Last Edit: September 24, 2019, 01:10:01 PM by ta0 »
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #9 on: September 25, 2019, 08:49:11 AM »

Are you sure that there is slipping of the tip ?
Has this ever been observed, or it is just a theoretical deduction ?
I too read similar statements, but I am doubtful.  I don't have the sensation that the tip slips, while the top spins, nearly always.
Do you know whether this was empirically demonstrated and documented ?

For a top leaning significantly and making a clear circular path on a flat surface, it's easy to determine by calculating the rolling condition (zero speed for the point of the sphere touching the surface).

If the tilt angle is alpha and the top is spinning at an angular velocity w and precessing at u, the pure rolling condition is:

w sin(alpha) r = u R

where the radius of the circle described by the precession is R and the radius of the tip r.

If the left side is bigger, then the tip is slipping while pushing the top forward. If the right side is bigger, the slipping friction is stopping the precession.

I always assumed the first case was generally true, but a back of the envelope calculation for one of my tops gave me that it's not so obvious  :-\

This makes me curious.  I think I will try an experiment to measure it.  Thanks for the formula.
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Jeremy McCreary

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Re: Three experiments with gyroscopes
« Reply #10 on: September 26, 2019, 04:01:50 AM »

But on a rotating tip (where the tip is rotating faster than it would be by rolling without slip) the sliding friction force will be in the opposite direction!
Are you sure that there is slipping of the tip ?
Has this ever been observed, or it is just a theoretical deduction ?
I too read similar statements, but I am doubtful.  I don't have the sensation that the tip slips, while the top spins, nearly always.
Do you know whether this was empirically demonstrated and documented ?

I see and hear a lot of "positive slip" in my tops. This occurs when travel speed is below that needed for pure rolling at the spin rate involved. A car accelerating on ice with lots of wheel spin is in a state of positive slip.

My smaller tops with ball tips routinely start out in positive slip after high-speed launches. The first top in the video below is a case in point. Skip to 1:42...

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

The top is in positive slip for the first 20 s or so after release at 1:55. You know it's slipping because the audible spin decay proceeds with little regard for the top's varying travel speed. Rolling regeneration becomes effective only when the tip rolls without slip. The top finally spins down to the pure rolling state sometime after 2:15.

Anyway I am not sure that sliding friction could make the top to rise.

It's certainly possible in theory. Most mathematical treatments of tops with ball tips (including tippe tops) get self-righting behavior by assuming some form of sliding or static Coulomb friction. Viscous friction models also lead to self-righting. The friction force is proportional to slip rate in the viscous model and independent of slip rate in the sliding Coulomb model. In the static Coulomb model, there is no slip -- just pure rolling.

In positive slip, it would be reasonable to model total tip resistance as a combo of sliding Coulomb friction + rolling resistance. Problem is, no one seems to know how to model the latter.
« Last Edit: September 26, 2019, 04:53:45 AM by Jeremy McCreary »
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #11 on: September 26, 2019, 08:41:19 AM »

Jeremy,

the issue is about the reason that make tops rise, (you show a Topnosis style top which of course can slip if you move the spinning surface in that way).
As Ta0 says, "The ball tip pushes the top forward in its precession, and that's the conventional explanation of why a top sleeps".
I am doubtful because I don't see, (or hear), the tip slipping in my tops.

You say, "A car accelerating on ice with lots of wheel spin is in a state of positive slip."
If this is what you mean, ok, but this happens only for a very little time after the top is spun. In the case of my tops, for probably less than one second.
Of course I have no problems in understanding that a positive slip makes the top rise.
The problem is that this acceleration lasts for too little time, and the top instead continues to rise for even minutes.

If there is slipping for a long time, (which I doubt), I think that the reason cannot be the inertial resistance of the top, (like it would be in the case of your example of the car accelerating on ice).  There should be another reason.

First I will want to verify whether this prolonged slipping really exists, then, in case, I will think to what it could be and why.   
« Last Edit: September 26, 2019, 08:55:40 AM by Iacopo »
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Jeremy McCreary

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Re: Three experiments with gyroscopes
« Reply #12 on: September 26, 2019, 12:34:01 PM »

the issue is about the reason that make tops rise, (you show a Topnosis style top which of course can slip if you move the spinning surface in that way).

I'd say that the top in the video stayed in positive slip as long as it did in spite of arena motions -- which most of the time acted to boost the tip's travel speed.

Of course, higher travel speed means pure rolling at a higher spin rate per the rolling condition. But in the video, spin rate still had to decay from its high launch value to a "rolling range" of spin rates compatible with pure rolling at observed travel speeds. Once slip vanished and pure rolling set in, the coefficient of Coulomb friction jumped from the kinetic (sliding) value to its higher static value. In drag racing lingo, the tip "caught", or "hooked up" at that point. And it tended to stay hooked up thereafter.

Granted, the tip "skidded" -- i.e., went into negative slip -- now and then when I tilted the arena too much. But once the spin rate was in rolling range, the tip was quick to hook up again. This occasional negative slip would never have happened without arena tilting, but I don't think it's relevant to the issue at hand.

You say, "A car accelerating on ice with lots of wheel spin is in a state of positive slip." If this is what you mean, ok, but this happens only for a very little time after the top is spun. In the case of my tops, for probably less than one second. Of course I have no problems in understanding that a positive slip makes the top rise.
The problem is that this acceleration lasts for too little time, and the top instead continues to rise for even minutes.

In answer to your empirical question to ta0, I was just sharing my own observations: (a) Positive slip is common in some tops and (b) lasts a good while after launch in some cases. I should have mentioned that I also see this on fixed table tops.

I think we agree that the contact forces present during positive slip are likely to contribute to self-righting while they last. We also agree that positive slip is just one of several contact processes involved. Their relative contributions may well evolve as spin-down proceeds.
 
If there is slipping for a long time, (which I doubt), I think that the reason cannot be the inertial resistance of the top, (like it would be in the case of your example of the car accelerating on ice).  There should be another reason.

Not sure which inertia(s) you mean here. If the tip has any traction at all, with or without slip, changes in travel speed will be opposed by both translational inertia (as measured by mass) and rotational inertia (as measured by AMI in this case). In the real world, slip diminishes the AMI's contribution but doesn't eliminate it.

Nothing mysterious about prolonged positive slip in my tops. Like a dragster, they sometimes launch with way too much spin for the rolling condition to hold. The greater the AMI, the longer it takes for available braking torques about the spin axis to bring the spin rate down to the rolling range.

Unfortunately, it's more complicated than that, as greater AMI also makes it harder to achieve a high launch rate with a given starting method. Your AMIs are generally much greater than mine. And I think your spin rates are often lower on final release. Both are especially true in my small tops most prone to prolonged positive slip. Yet these tops also tend to self-right when the tip's radius of curvature is large enough and the CM height low enough. As I recall, the self-righting starts during the positive slip phase and continues thereafter.

These inertial and dynamic differences could have a lot to do with the differences in our observations.
« Last Edit: September 26, 2019, 01:16:49 PM by Jeremy McCreary »
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #13 on: September 26, 2019, 01:34:37 PM »

I'd say that the top in the video stayed in positive slip as long as it did in spite of arena motions -- which most of the time acted to boost the tip's travel speed.

You mean that the top slips forward, along the temporary descents of the arena... ? (Since it is the arena that pushes and makes the top to spin).

Not sure which inertia(s) you mean here. If the tip has any traction at all, with or without slip, changes in travel speed will be opposed by both translational inertia (as measured by mass) and rotational inertia (as measured by AMI in this case). Slip diminishes the AMI's contribution but doesn't eliminate it.

I meant translational inertia.  The rotational inertia is the one keeping the tip spinning against translational inertia so it slips.

Nothing mysterious about prolonged positive slip in my tops... 
These inertial and dynamic differences could have a lot to do with the differences in our observations.

Maybe you are right.
For how much time your tops can stay slipping, after you launch them ?
I suspect that there is something else happening, that is not exactly positive slipping, which I am going to explain in the next comment.
« Last Edit: September 26, 2019, 01:37:49 PM by Iacopo »
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #14 on: September 26, 2019, 03:57:59 PM »

D.G. Parkyn, ("The rising of tops with rounded pegs"), made an experiment which seems to prove a case of positive slipping of the top.
The track left by the top, (photo), in fact, resulted a bit shorter than it should have been, given the dimensions of the tip and the angle of tilting of the top.
The results, for some revolutions of precession, were:

Calculated    Observed
  rolling          length
 distance
   191              191
   186              186
   178              179
   199              190
   167              160
   156              154



Anyway I am not convinced.

For the first two revolutions of precession the numbers are the same, so there was not slipping at the beginning, the acceleration phase was already completed.  Since, then, the angular spin speed of the top is in constant deceleration, how could this produce acceleration and slipping, starting from the fourth revolution of precession ?  This doesn't make sense to me.

I think there is a better explanation;
Looking at the track in the photo it can be seen that the track is dotted, meaning that the top was unbalanced, (tip off centered).
I don't know why an unbalanced top was used, maybe at that time precision spinning tops didn't exist.
Being the tip off centered, and the top tilted, the top walked making little jumps, for this reason the left track is dotted.
Because of this, the angular velocity of the precession could not be constant; during the jump, the top was in mid air, so for an instant there was not precession.
The lack of precession while in mid air makes the linear speed of the tip to be lower than when it is in contact with the spinning surface.
For this reason the tip has a "positive slip" when it is in mid air, so the track is shorter than expected.

But this is a particular and deceitful dynamics due to an unbalanced top.  It is not a case of a top accelerating the precession. 
 
   
« Last Edit: September 26, 2019, 04:02:15 PM by Iacopo »
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