EULER's disc and persistent ROCKING PLATES. How does GRAVITY make them work ?

[Mike Smith Cosmos]

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Parts of the heavy steel disc, appear to keep falling under gravity towards the level mirror surface . See picture.

The disc appears to keep falling around its circumference , but never makes it. So the disc continues to spin a long time. ( Not really a spin , more a slow turning as the fast falling oscillations occur. )

 

I have noticed : occasionally if china dishes are haphazardly laid on a hard granite surface , one plate will occasionally , rock back and forward almost indefinitely , going click, click, click.....again sides of the plate falling this side then that side , this side then that side .

 

How does Gravity ? if it is gravity that causes both these phenomenon , do this ?

 

Is there anything to learn about gravity by these sightings ?

 

Mike

 

Ps . Originally discovered by the celebrated Mathematician .. Euler .

Edited April 8, 2015 by Mike Smith Cosmos

[ajb]

I don't think this experiment tells us much about gravity. Over the distance scales involved here we can take the acceleration due to gravity to be constant.

 

I also don't think the mechanics here is very well understood, but Keith Moffatt has a reasonable model. The main source of energy dissipation is due to surface friction. There have been various experiments here. What is does show is that seemingly simple mechanical situations can be hard to model.

[swansont]

The "ringdown" of Euler's disk takes a long time because the contact area is small and there is very little friction and it's rotating, so there's some gyroscopic motion involved. It doesn't happen if you just drop the disk. So it's not gravity, per se, that's the culprit here, it's the gyroscopic motion and energy dissipation.

[Strange]

In a way, it a more complex version of a pendulum: the force of gravity tries to bring the object (disk, plate, pendulum bob) to a minimum energy state, but inertia makes the object it overshoot and so gravity then pulls it back the other way. Without friction or other energy losses you would have a perpetual cycle of restoring force -- overshoot -- restoring force -- overshoot ...

[imatfaal]

!

Moderator Note

 

Mike I have hidden your most recent post.

 

It is way off topic. You were given permission to open a topic to ask how an Euler's Disc can be modelled/understood - within half a dozen posts you are introducing the moon. Please stick to the topic.

 

[Mike Smith Cosmos]

 

In a way, it a more complex version of a pendulum: the force of gravity tries to bring the object (disk, plate, pendulum bob) to a minimum energy state, but inertia makes the object it overshoot and so gravity then pulls it back the other way. Without friction or other energy losses you would have a perpetual cycle of restoring force -- overshoot -- restoring force -- overshoot ...

How will Eulers Disc respond to the gravitational influences from the earths gravity below and any other forces ?

 

What model can I use

 

Mike

Edited April 8, 2015 by Mike Smith Cosmos

[ajb]

How will Eulers Disc respond to the gravitational influences from the earths gravity below and any other forces ?

 

What model can I use

 

Moffatt's analysis can be found below. I don't know exactly how this analysis is viewed, a quick google suggest that not everyone agrees with him. Anyway, I suggest you start with that work.

 

http://users.uoa.gr/~pjioannou/mechgrad/DynaPage.pdf

 

Earth's gravity does appear essential here, but only in the way it usually does with such mechanical models; g = 9.81m/s^2.

 

Other forces would usually be taken to be negligible. I don't see why you could not consider a charged disk etc. other than it is probabily hard to model.

[Strange]

There is a summary of various approaches to this (with links) here: http://tetrahedral.blogspot.co.uk/2011/03/eulers-disk.html

[John Cuthber]

How will Eulers Disc respond to the gravitational influences from the earths gravity below and any other forces ?

 

What model can I use

 

Mike

There's nothing magical about gravity. In this case it can be modelled very simply as a constant force acting at the centre of the disk, directly downwards and equal to 9.81 times the mass of the disk (in kilograms).

[swansont]

How will Eulers Disc respond to the gravitational influences from the earths gravity below and any other forces ?

 

What model can I use

 

Mike

 

It's a constant force, directed down. F = mg

 

edit: sorry there's an echo in here

[imatfaal]

Accepting that gravity is the simple bit of this observation...

 

and without looking at the competing explanations - it's conservation of angular momentum isn't it? The only external torques are a rolling friction between a sharp metal edge and a sheet of glass (ie very very little) and air resistance which at such low speeds is gonna be negligable compared to the amount of ang mom.

[swansont]

Accepting that gravity is the simple bit of this observation...

 

and without looking at the competing explanations - it's conservation of angular momentum isn't it? The only external torques are a rolling friction between a sharp metal edge and a sheet of glass (ie very very little) and air resistance which at such low speeds is gonna be negligable compared to the amount of ang mom.

 

Gravity exerts a torque, which is why you will see the disc precess.

 

I think this is related to the wobbling plate problem that famously got Feynman started on the solution to QED (a wobbling plate will also precess), except that the plate is not constrained to move with one point on the surface.

 

Here's a link that has info on both situations

http://ruina.tam.cornell.edu/research/topics/miscellaneous/rolling_and_sliding.php

 

And another on the plate

http://demonstrations.wolfram.com/FeynmansWobblingPlate/

 

(the upshot here being that this is a solved problem - no new physics here — even though it's a tad complicated)

[imatfaal]

I am a bit lost. But I think that I am getting there. I was thinking that gravity acts as if at a point coincident with the axis of spin and thus no perp distance and no torque - AND - that gravity acts parallel to the axis of the roll and thus again no torque. But there is also the normal which would be equal to mg.cos(theta).r which would act at the rim. Am I barking up the wrong tree?

[swansont]

I am a bit lost. But I think that I am getting there. I was thinking that gravity acts as if at a point coincident with the axis of spin and thus no perp distance and no torque - AND - that gravity acts parallel to the axis of the roll and thus again no torque. But there is also the normal which would be equal to mg.cos(theta).r which would act at the rim. Am I barking up the wrong tree?

 

 

There's got to be a torque exerted by gravity, as it will act on the center of mass, and the pivot point is the edge. But the system is not rotating in a way that the rotation and the symmetry of the object line up, which is a tad confusing to me. The coin is both spinning and traveling a circular path, so there's an addition of two rotations. I've been spinning a novelty coin on my desk trying to get this straight in my head.

 

Here's another link I've found. The analysis is a tad complicated

 

http://www.real-world-physics-problems.com/eulers-disk.html

 

From looking at the abstract of the Nature article, it looks like they analyze the movement of the contact point

http://www.nature.com/nature/journal/v404/n6780/fig_tab/404833a0_F1.html

 

Another summary of a published paper on the topic

https://croor.wordpress.com/2010/11/07/eulers-disk/

[imatfaal]

Ah - first thing to note. I was refering (meaning to refer) to torques opposing angular momentum of the disc which I have as spinning about central axis of disc and rolling around a point on table. But as you put it there are clearly other torques on the disc - gravity acting at centre with pivot at touch point

second thing

 

Although the model here neglects friction, Euler's disk cannot be modeled as a conservation of angular momentum problem. This is because there is a net moment (torque) acting on the disk about its center of mass G (due to the contact force F_AZ between disk and surface, at point A).

 

From your first link - so the normal force ie mg.cos(theta).r will screw any attempts to work this out as an ang mom problem (apparently) . I will need to read a lot more...

[swansont]

 

From your first link - so the normal force ie mg.cos(theta).r will screw any attempts to work this out as an ang mom problem (apparently) . I will need to read a lot more...

 

That may be the key. This is not the same as assuming there is no energy loss. Without the contact force, this doesn't work. (I had already convinced myself that angular momentum couldn't possibly be conserved, but hadn't gotten to this point yet)

[imatfaal]

 

... I've been spinning a novelty coin on my desk trying to get this straight in my head...

 

 

You've got lasers and atomic clocks and everything and you are spinning a novelty coin on your desk; appropriate resources and get measuring.

 

This is probably why I could never be a researcher of any form

[Mike Smith Cosmos]

. Now experiment using a china ( not plastic ) saucer on a steel knife blade on a granite level work top, or on top of an even bigger china plate , no knife needed as a fulcrum here . You should be able to locate an irregularity for a fulcrum . Suddenly it will oscillate !

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Balance well ' to taste '

 

Mike ( now isn't this fun ! )

Edited April 8, 2015 by Mike Smith Cosmos

[swansont]

Mike, in response to your inquiries made outside this thread: The motion involved is due to the effects that we have discussed here in this thread: torques and angular momentum. It is not due to any novel actions of gravity. Gravity is modeled as imparting a constant acceleration, as three different people have explained. The physics stemming from that explains the motion.

[Mike Smith Cosmos]

In a way, it a more complex version of a pendulum: the force of gravity tries to bring the object (disk, plate, pendulum bob) to a minimum energy state, but inertia makes the object it overshoot and so gravity then pulls it back the other way. Without friction or other energy losses you would have a perpetual cycle of restoring force -- overshoot -- restoring force -- overshoot ...

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.This is sort of what ' I wondered or thought might be going on.' Not as a NOVEL effect , so much as a relatively very , very , CONSTANT effect for the time period of oscillation of the plate or rotation of the disc. But in a very precise , and very constant way . ( that is over the time period of one oscillation of the plate , or one rotation of the Euler Disk ). Not being privy to fluctuations in longer time going on due to the different times and paths taken by the influence of gravity , say coming from churning , molten iron core material, or moon 'wobble' or sun 'heaving' .

 

This seemed to remind me of a Richard Feyneman lecture on light reflection from a mirror surface . Where he explained about ALL the possible paths , with there different probabilities paths being taken , but when all added taken into account ( the angle of incidence = angle of reflection was the one that dominated ) even though the other paths existed.

 

Surely the high degree of stability of Gravity ( over comparatively short periods of time) , must play its part in this model , both in a stable restorative torque , as well as very constant, holding the model together on the surface of its operation?

 

Mike

Edited April 9, 2015 by Mike Smith Cosmos

[ajb]

Surely the high degree of stability of Gravity ( over comparatively short periods of time) , must play its part in this model , both in a stable restorative torque , as well as very constant, holding the model together on the surface of its operation?

Like in most of these mechanical problems, the force due to gravity changes so little over the vertical distances and the time scales involved that you can ignore them; including gravitational waves, local changes in density, tidal forces on your disk etc. Other systematic and random errors will be more important in you analysis of the experiment than any changes of gravity.

[imatfaal]

 

Here's another link I've found. The analysis is a tad complicated

 

http://www.real-world-physics-problems.com/eulers-disk.html

 

This seems to be the best description of the motion - rather than analysis of the final stages per the Nature article. But the assumptions it makes in order to make the maths wieldy seem to be almost contradictory - I presume this is acceptable but it grates rather.

 

The analysis concludes "This informative result tells us that as θ→0, w_p goes to infinity." which does indeed follow from the model which is premised on the change in rotational acceleration with respect to spin and roll as the angle theta decrease. The angle theta must slowly decrease as the energy is robbed from the system due to dissipative effects of friction and air resistance and thus the centre of mass falls and gpe diminishes. But the whole analysis is also based on setting the effect of friction and air resistance to zero.

 

It seems contradictory to say in one breath that the friction/air resistance can be safely ignored as insignificant (to the angular accelerations) but in the next breath use the fact that the friction/air resistance are the agents of the change.

 

It is not as if these are forces act such that they cannot influence the component of the motion in question - the frictional force is tangential at a perpendicular distance to the axis of rotation. The force is enough to change the angle of the coin and slow the whole system - but not enough to affect the angular velocity. Either I am reading it wrong or this seems hoopy.

[swansont]

 

This seems to be the best description of the motion - rather than analysis of the final stages per the Nature article. But the assumptions it makes in order to make the maths wieldy seem to be almost contradictory - I presume this is acceptable but it grates rather.

 

The analysis concludes "This informative result tells us that as θ→0, w_p goes to infinity." which does indeed follow from the model which is premised on the change in rotational acceleration with respect to spin and roll as the angle theta decrease. The angle theta must slowly decrease as the energy is robbed from the system due to dissipative effects of friction and air resistance and thus the centre of mass falls and gpe diminishes. But the whole analysis is also based on setting the effect of friction and air resistance to zero.

 

It seems contradictory to say in one breath that the friction/air resistance can be safely ignored as insignificant (to the angular accelerations) but in the next breath use the fact that the friction/air resistance are the agents of the change.

 

It is not as if these are forces act such that they cannot influence the component of the motion in question - the frictional force is tangential at a perpendicular distance to the axis of rotation. The force is enough to change the angle of the coin and slow the whole system - but not enough to affect the angular velocity. Either I am reading it wrong or this seems hoopy.

 

It's not a problem if they aren't analyzing the time-dependent behavior, and are only analyzing the angle-dependent behavior. The time-dependent behavior depends on dissipation, but ignoring that only means they aren't predicting how long the system will take to come to rest (which may end up being an exponential function anyway, so the time would be infinite) The angle dependent behavior is like taking a very short glimpse of it and then mentally looping it like a gif.

[imatfaal]

 

It's not a problem if they aren't analyzing the time-dependent behavior, and are only analyzing the angle-dependent behavior. The time-dependent behavior depends on dissipation, but ignoring that only means they aren't predicting how long the system will take to come to rest (which may end up being an exponential function anyway, so the time would be infinite) The angle dependent behavior is like taking a very short glimpse of it and then mentally looping it like a gif.

 

Ok - that makes sense. I hadn't separated the two concepts in my head.

 

So the analysis works out the angular velocity at any given angle - if we had a frictionless surface and set the coin spinning at any theta from the horizontal this model would give us the corresponding angular velocity. How we get to theta is not included in the model. But we know, absent any info in the model, that theta will tend to zero and can thus give the change in angular velocity as this happens. OK - almost reconciled in my head.

[Mike Smith Cosmos]

Like in most of these mechanical problems, the force due to gravity changes so little over the vertical distances and the time scales involved that you can ignore them; including gravitational waves, local changes in density, tidal forces on your disk etc. Other systematic and random errors will be more important in you analysis of the experiment than any changes of gravity.

I have got the EULER's disk out of its box and cranked it up a number of times.

Although a slight twist is necessary to start the disc operating , by a fall at an angle.

Once it has started its ' spoll' ( spin and roll ), it is clear that spinning is not a dominant characteristic . I have measured it as changing between 1/3 rotation/ sec to a 1 rotation per second . Though it appears very active . This is the up and down bounce as one side is falling to the surface and the other side of the circle is bouncing up . It is the point of bounce ( surface contact ) that is rotating, also . But a mark on the disc can be seen to be rotating fairly slowly compared to the other fast movement of the oscillating bounce ( approximately 10 times per second ) .

 

So one should ask if the angular velocity is so slow ( 1 rev per sec) to ( 1/3 rev per second ) can angular momentum , be the dominant characteristic , whereas the oscillating mass bounce ( 10 Hz and rising ) and roll seems to be where all the action is. Is this bounce not the falling to the surface under the pull of gravity , and the return force not the leverage of the base it is rolling on giving the upward thrust to push the restoring movement of the disc?

 

Could it not be argued, that it is the fast up and down rolling bounce due to gravity , that is the key player in the Euler Disk phenomenon rather than the fast spin or angular momentum usually attributed to the stability of a spinning top? As 1/3 to 1 revs/ sec is very slow and would normally topple . Or have I got it wrong ?

 

Mike

 

Ps this fast up and down bounce , is reminiscence of a Ping pong ball getting trapped between bat and table at a couple of inches to one inch . The Ping pong ball rattles rapidly with a zzittt .

Edited April 9, 2015 by Mike Smith Cosmos