Extracting energy from gyroscope precession

[Precision99]

Seems like this poster isn't interested in the law of conservation of energy.


Intuitively I think of examples like a hula-hoop where you can accelerate or decelerate its rotational speed without exerting any direct rotational torque. I have a feeling this example is masking a similar concept.

Presumably I am "this poster"? Nothing I have said contradicts conservation of energy, does it?

Re a hula-hoop, you are exerting forces directly on the hoop, on the rim of the "wheel", so you are indeed exerting rotational torque and we should therefore not be surprised that we can accelerate or decelerate it's rotational speed.

 

[Precision99]

please point me to the frictionless bearings and the part where anything spinning in air has no frictional losses .... my credit card is ready ...

We can carry out the experiment in vacuum to eliminate wind drag. Of course there is no such thing as a perfectly frictionless bearing. I'm not suggesting that. But in Physics, and in though experiments, we often visualise an idealised case without friction to help us understand the basic concepts.

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... but I believe that a machine CAN be made, with frictionless bearing, where a torque CAN be transmitted to a rotor, and the rotor be thus made to rotationally speed up. And without cheating like using magnetic forces (electric motor) or wind forces (turbine wheel) or any other cheating nonsense where something mechanically touches the rotor, or where a magnetic or electric or any other sort of field produces a force on the rotor. And no use of gravity, either. Just by appropriate machine design, and appropriate forced motion of the axle. Anyone care to comment on that?

I'm listening.

I'm not claiming anything that would contradict well established physics. Just some interesting (at least to me) examples. I have 3 such examples, but will start with a child's swing. This is a rotational system. The ropes or rigid bars form the "spoke", and the axle is the pivot at the top of the swing. The rotational bearing at the top can be considered frictionless, and nothing touches or exerts a force on the rotating object, being the seat, the rods from the seat to the pivot, and the person on the swing.

But here is the curious part. We all know that the child (and even an adult!) can get the swing into rotational motion just with appropriate body movements and muscle forces. One can build up the swing's motion without limit. And if rigid rods are used rather than ropes, then it would be possible to build up the motion so that the seat and person on the seat went around and around, true rotary motion, built up from nothing, and without any external torque being exerted on the system.

Does anyone else find this example quite curious? Where has the torque come from to get the swing rotating, given that the only thing that physically touches it is a frictionless bearing at the top of the swing. Does this mean that a bicycle wheel on frictionless bearing can after all be rotationally sped up, without an external force or torque acting on the wheel? But I said in previous postings that that was impossible. Is it? We would appear to have a contrary example.

What say you to all of this, Kajunbee, as I sense that you understand what I'm talking about. Or anyone. Is the principle of conservation of angular momentum in trouble?

 

[Easy peasy]

it's not built up from nothing - the friction in the system allows the swing user to impart momentum ... and therefore build up the swing oscillation ...

 

[Precision99]

it's not built up from nothing - the friction in the system allows the swing user to impart momentum ... and therefore build up the swing oscillation ...

Incorrect. Swings do not in any way rely on friction.

But I can think of examples where your friction idea is sound. For example, if you sit on a rotatable office chair, then by appropriately twisting and moving your body, you can make it jerkily rotate around and around in one direction, and in that case you are exploiting friction in the pivot. Likewise, you can make a skateboard travel indefinitely in a single direction, in a jerky motion, along a flat surface just by appropriate body movements, and exploiting friction in the bearings, and rolling loss in the wheels. But that is not how a swing works.

 

[std_match]

Quite so. We are completely in agreement, but noting that the "opposing force" is at right angles to your movement of the axle, so no work is done. Indeed, strictly speaking, the gyroscopic effect does not "oppose" your motion of the axle at all, because there is no component of opposing torque in the direction of your angular movement of the axle.

The movement is never perpendicular to the external force.

 

[Kajunbee]

We can carry out the experiment in vacuum to eliminate wind drag. Of course there is no such thing as a perfectly frictionless bearing. I'm not suggesting that. But in Physics, and in though experiments, we often visualise an idealised case without friction to help us understand the basic concepts.

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I'm not claiming anything that would contradict well established physics. Just some interesting (at least to me) examples. I have 3 such examples, but will start with a child's swing. This is a rotational system. The ropes or rigid bars form the "spoke", and the axle is the pivot at the top of the swing. The rotational bearing at the top can be considered frictionless, and nothing touches or exerts a force on the rotating object, being the seat, the rods from the seat to the pivot, and the person on the swing.

But here is the curious part. We all know that the child (and even an adult!) can get the swing into rotational motion just with appropriate body movements and muscle forces. One can build up the swing's motion without limit. And if rigid rods are used rather than ropes, then it would be possible to build up the motion so that the seat and person on the seat went around and around, true rotary motion, built up from nothing, and without any external torque being exerted on the system.

Does anyone else find this example quite curious? Where has the torque come from to get the swing rotating, given that the only thing that physically touches it is a frictionless bearing at the top of the swing. Does this mean that a bicycle wheel on frictionless bearing can after all be rotationally sped up, without an external force or torque acting on the wheel? But I said in previous postings that that was impossible. Is it? We would appear to have a contrary example.

What say you to all of this, Kajunbee, as I sense that you understand what I'm talking about. Or anyone. Is the principle of conservation of angular momentum in trouble?

Would you still be able to swing if the ropes were replaced with rigid rods.

 

[Precision99]

The movement is never perpendicular to the external force.

I don't understand your sentence, so don't know if I agree or not. Can you elaborate? And we are all still waiting to know exactly how you would use a (very large) spinning "bicycle wheel" to harness the rotational energy of the earth.

But I do stand by everything that I have said re forces (or torques if you prefer) being at right angles when you change the orientation of the axle of a spinning bicycle wheel. But I might not have made it clear, so will explain in more detail.

Hold the axle of your spinning bike wheel (one hand supporting each end) so that the axle is horizontal. Now, change the orientation of the axle by rotating it in the horizontal plane. A hefty reaction force will be produced, trying to lift one end of the axle, and lower the other end. These vertical forces on the ends of the axle are at right angles to your horizontal movement of the ends of the axle, and therefore you do no work in rotating the axle in the horizontal plane. If you don't believe me, try it. And actually, this must be the case, because if the axle genuinely resisted your altering of it's orientation (rather than producing a force at right angles) then you would be doing work against that resistance. And then physics would be in real trouble. Where would the work done end up? As explained previously, it can't end up increasing the rotational speed of the wheel, because no torque can be transferred through the bearing to the wheel to speed it up.

So, do you agree with what I wrote above?

 

[Precision99]

Would you still be able to swing if the ropes were replaced with rigid rods.

Yes. In fact it's even better.

With ropes or chains, then you are limited to winding up the swing until the ropes become horizontal, and after that they lose their tension and you can't wind up any further. Hey, every kid knows that! When I was a kid, I sure as heck tried to see how high I could swing, and can assure you that if you try too hard then the chains become slack at the top of the stroke, and you can go no further. And it also gets a bit scary once the chains start getting slack as they approach horizontal.

But with the ropes replaced by rigid rods, this limitation is removed, and it is possible to crank the swing up and up until you start doing full circles. I have not personally done or witnessed this, but have read that this is the case, and has been observed.

 

[Easy peasy]

Dear precision99, apart from bare assertion - can you offer proof that friction does not assist in getting a swing started - ...?

 

[FvM]

The swing example is inappropriate for the original gyroscope problem. Swing involves periodical transfer between potential and kinetic energy. Work is done by weight shift which dynamically changes the moment of inertia.

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I have however learned that friction plays a role in the energy transfer between gyroscope rotation and external work in a gyroscopic exercise tool, see https://en.wikipedia.org/wiki/Gyroscopic_exercise_tool

 

[Precision99]

Dear precision99, apart from bare assertion - can you offer proof that friction does not assist in getting a swing started - ...?

Well to be honest, as it was you that said that friction is the key mechanism in getting a swing started, then the onus is on you to show how it does so. You did not show this, so how on earth can I refute that which you never explained in the first place. You provided no explanation to refute.

But I did try to help by providing two examples where friction is exploited to give the appearance of a reactionless torque or force.

I can explain how a swing does work, but to do that prematurely would rob others of the pleasure of thinking about this stuff. Be patient and the explanation of how a swing works will be revealed in the discussions, and I confidently predict it will be found that friction does not play a part. But if you think it does then please elaborate on the mechanism.

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The swing example is inappropriate for the original gyroscope problem. Swing involves periodical transfer between potential and kinetic energy. Work is done by weight shift which dynamically changes the moment of inertia.

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I have however learned that friction plays a role in the energy transfer between gyroscope rotation and external work in a gyroscopic exercise tool, see https://en.wikipedia.org/wiki/Gyroscopic_exercise_tool

Agreed that a swing is quite different to a gyroscope, but I thought it was an interesting example to bring up. A moving swing does indeed involve periodical transfer between potential and kinetic energy. But while that is a true statement, it does not in itself explain how a swing is "wound up"" from rest. In my view you are on the right track in speaking of weight shift, but you would need to explain how dynamically changing the moment of inertia acts to wind up the swinging motion. I do note that if the swing starts from stationary, then you can dynamically change the moment of inertia all you like by lifting yourself higher or lower in the seat, but that in itself won't get the swing moving.

And now to the gyroscopic exercise tool! It was that damn thing that, about a fortnight ago, got me thinking about this stuff in he first place. A work colleague of mine, actually an applied mathematician, had one and chanced to mention to me that the rotor was rotationally accelerated to high speeds just by gyrating the axis of rotation with your wrist. I immediately said that if the rotor runs on low-friction bearings as per a bicycle wheel, then it was impossible, because a bearing cannot transmit torque to the rotor that spins on the bearing, as I have hammered to death in previous postings. My mate grinned and invited me to try it out for myself. So who was right? Let me tell you, I did not sleep at all that night until I figured out how it worked. And I was right. Some fun discussions to be had here.

 

[Kajunbee]

Yes. In fact it's even better.

With ropes or chains, then you are limited to winding up the swing until the ropes become horizontal, and after that they lose their tension and you can't wind up any further. Hey, every kid knows that! When I was a kid, I sure as heck tried to see how high I could swing, and can assure you that if you try too hard then the chains become slack at the top of the stroke, and you can go no further. And it also gets a bit scary once the chains start getting slack as they approach horizontal.

But with the ropes replaced by rigid rods, this limitation is removed, and it is possible to crank the swing up and up until you start doing full circles. I have not personally done or witnessed this, but have read that this is the case, and has been observed.

Oh yeah, have actually broken the chains attempting to go all the way over. A few years ago I had thought about this very subject. I had always assumed as a kid that pumping my legs back and forth was making me go ever higher. Too prove it I jumped on the tree swing I had made for the kids. I found that I was still able to swing without pumping my legs at all. But you still have to lean back against the chains on down swing. When you do this it puts a bend/angle in the chain. Now how or whether that increased angle effects the swing motion I'm not sure. But it seems to me it would have some impact. Most likely there was something else going on that I was not taking into account.

 

[Easy peasy]

the bend angle in the chain does indeed help establish motion - have you ever thought how one is able to start a swing from zero motion - without friction .?

it should be clear to even a casual observer that without friction, getting a swing started is a near impossible scenario - wind resistance will assist too...

 

[Precision99]

the bend angle in the chain does indeed help establish motion - have you ever thought how one is able to start a swing from zero motion - without friction .?

it should be clear to even a casual observer that without friction, getting a swing started is a near impossible scenario - wind resistance will assist too...

the bend angle in the chain does indeed help establish motion - have you ever thought how one is able to start a swing from zero motion - without friction .?

it should be clear to even a casual observer that without friction, getting a swing started is a near impossible scenario - wind resistance will assist too...

I find your posting confusing. First you say that the bend angle in the chain helps establish motion. And then you say that without friction, it is effectively impossible to get a swing started. That's a contradiction.

So which is it that is necessary to get the swing started, bending the chain, or friction? First you say one, then the other ...

I would claim that neither are necessary, either to get the swing initially started from stationary, or to subsequently "pump up" the amplitude of the oscillations. Anyone else agree (or disagree) with this?

If you accept that swings with rigid rods can be started from rest and then pumped up, then clearly "bending the chain" is not strictly necessary for operation of a swing, though it may be a player when and if chains are used.

And I can assure you, that you can refine the design of a swing to make the friction in the top bearing vanishingly small, and the swing will operate just as well. If you use very thin rope, or very fine steel cable, then the "bearing" at the top is the flexing of the said rope or cable, and any effective "friction" will be exceedingly small,, but the swing will work just as well. Nope, friction is not a player in the operation of a swing.

 

[Easy peasy]

I find your posting confusing. First you say that the bend angle in the chain helps establish motion. And then you say that without friction, it is effectively impossible to get a swing started. That's a contradiction.

No contradiction at all - I realise there is friction in a real system that assists starting ... I suggest a primer in logic ... the bend angle assists imparting momentum ONCE you have started swinging - the friction also assists ...

You have ignored the fact that there is net zero momentum at rest, this is what requires friction to form an offset force - have you a degree in mechanical engineering by any chance ... ? if not please find a fellow who has and they can explain the nuances of frictionless systems ...

 

[Precision99]

I have however learned that friction plays a role in the energy transfer between gyroscope rotation and external work in a gyroscopic exercise tool, see https://en.wikipedia.org/wiki/Gyroscopic_exercise_tool

OK. So let's talk more about this infuriating device. I have one on my desk, and can assure you that it is possible to accelerate the rotor to amazing speeds just by gyrating your wrist. But I have also stated many times that that is impossible if the rotor spins on bearings.

And therefore this device puzzled me greatly initially and I lost a lot of sleep. But I trusted my knowledge of bearings completely, and thus was forced to conclude that the shaft cannot run on bearings. And sure enough, when I looked in detail at how the thing is built, the rotor does not spin on bearings at all, certainly not in the way that a bicycle wheel does. So here is how it is built, and how rotational torque is transferred to the rotor.

The rotor is locked to the shaft, so the entire shaft turns with the rotor. The ends of the shaft are turned down to a very small diameter, roughly 1 mm in diameter. But the ends of the shaft do not sit in bearings - if they did then the thing could not work. Instead, they sit in a circular track that runs around the periphery of the ball. The track, in effect, consists two annuli (an annulus is a flat disc with a hole in the centre), one above the other, vertically separated by about 1.2 mm so that the axle ends fit nicely between the upper and lower annular tracks. Let's say that the axle and the two annular tracks are in the horizontal plane. The axle is thus free to precess in the horizontal plane, and in doing so, the ends of the axles will run around the circular tracks that support the axle. And in doing so, the axle (and therefore rotor) is forcibly caused to rotate, due to friction between the track and the ends of the axle.

And so, the mechanism that turns and accelerates the rotor is found to be due to no more than a small diameter roller, running along a track. It is no more mysterious than pushing your car along the road, and observing that the wheels are forced to go around, due to friction between the wheels and the road. In the case of the gyro exerciser, the "wheels" are the ends of the axle, and only about 1mm in diameter, while the "road"" is the circular track that they run inside of, as described. And of course, the reason that the ends of the axle are turned down to such small diameter (1mm), is to ensure that the rotor is driven at high RPM for a modest speed of precession. Same thing with your car. Fit it with tiny wheels, and the wheels spin fast for a given road speed. And it is also clear that this device relies on friction between the "wheels" that are the ends of the axle, and the track on which there wheels run, just as with your car. That is why if you oil one of these gyro exercisers, it won't work, because there is not enough friction between the axle ends and the circular track in which they run.

So science, engineering and logic triumph. Knowing only how a bearing works (torque cannot be transmitted from stationary shaft, through a bearing to a rotor) one can logically deduce that the rotor in these gyro exercisers cannot be supported by bearings. And when the device is disassembled, this is indeed found to be the case. Engineering. Beautiful one day, perfect the next.

But again I will ask the question that I posed previously. Is it always true that you can't transmit torque and rotational acceleration to a rotor that is supported on frictionless bearings? Is the swing one such contrary example? Are there other examples as well?

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No contradiction at all - I realise there is friction in a real system that assists starting ... I suggest a primer in logic ... the bend angle assists imparting momentum ONCE you have started swinging - the friction also assists ...

You have ignored the fact that there is net zero momentum at rest, this is what requires friction to form an offset force - have you a degree in mechanical engineering by any chance ... ? if not please find a fellow who has and they can explain the nuances of frictionless systems ...

So let's be clear about your position. You claim that a swing cannot be "wound up"" from stationary without friction in the pivot at the top of the swing. Is that right? Yes or no.

You are perfectly correct in noting that there is net zero angular (and linear) momentum at rest, and I am acutely aware of that fact. Indeed, that is why I presented this example in the first place. And on the face of it you would appear to be right. How can angular (or linear) momentum be magically gained in a system that is frictionless with respect to the adjacent environment. This is precisely why swings are curious and interesting, because I can assure you that they do not rely on friction in the top pivot, noting that that is the only physical connection to the adjacent environment. Please find a swing and take the time to experiment with it. You will not be able to find any evidence that altering the friction in the top pivot makes the swing easier or harder to start and pump up. And, as I stated earlier, you can refine the pivot to have a vanishingly small amount of friction, and the swing will still function perfectly.

Your reasoning is completely valid for a rotatable office chair with a frictionless bearing. You can sit on the seat and gyrate your body all day in any way you wish, but you will not succeed in pumping up the rotation so that you and the chair end up rotating around and around, though you can do so if the bearing has friction. Presumably this is the model and reasoning that you are applying to a swing. And getting it wrong.

Here is something to think about. You are familiar with a pendulum. We can build a pendulum with essentially zero friction in the overhead pivot, and we can certainly analyse and understand the behavior of a frictionless pendulum. OK. So grab the pendulum bob, and lift it so that the rod or string is say 30 degrees off vertical. Hold the raised bob perfectly stationary. The angular and linear momentum is zero. Now let it go. It will gain angular momentum. Where has the torque come from to cause that angular acceleration? After all, by your reasoning, the pivot point is frictionless, so the torque cannot be being transmitted through the pivot. Is conservation of momentum being violated? Clearly this behaviour is quite different to that of a rotatable office chair. A swing is a type of pendulum, and what or is not possible is different to a rotatable office chair, upon which you appear to base your reasoning.

 

[std_match]

A swing can be started without friction.
We can move some part of the mass off-center (some other part will go off-center in the other direction).
If we then move this mass up/down with correct timing, we will add energy to the system, and the swing is going.

 

[Precision99]

A swing can be started without friction.
We can move some part of the mass off-center (some other part will go off-center in the other direction).
If we then move this mass up/down with correct timing, we will add energy to the system, and the swing is going.

Yes! Absolutely correct, and clearly and concisely expressed. Allow me to elaborate in more detail.

I can't add more to your correct explanation of how the first small movement is obtained, but then precisely how is it pumped up from there? By appropriate movement and bending of the body, the person raises their body (more precisely their centre of mass, CM) as they approach the top of the stroke. As you say, that adds energy to the system, obtained from the person's muscles. Then, as the swing moves downward, the person lowers the CM of their body, to a minimum at the bottom of the stroke, and thus the energy that was input by raising the CM is converted to kinetic energy. This process is repeated at every stroke, with the result that the swing amplitude is increased.

I presented this as an interesting example of how torque could be applied to a rotating component, even though the pivot of the said rotating component is frictionless. This particular example would not be possible without the use of gravity, although the torque and energy that are added to the system come from the person's muscles, not from gravity as such. This trick involving gravity cannot be played when sitting on a frictionless rotatable office chair, which is why you can gyrate and move and twist your body all you like on a frictionless office chair, but you will not alter the initial net angular momentum of zero, and not succeed in "winding up" the rotation.

But with the swing, the initial angular momentum is also zero, but in this case you really do increase the angular momentum and rotational kinetic energy of the system. How can this be? Where can the net torque required to do this come from, given that the pivot to which the swing is connected is frictionless? I never ask a question unless I know the answer, but I won't answer that question because others may enjoy thinking about it.

And with rigid rods instead of ropes, there is no reason why the swing can't be pumped up until the terrified occupant goes around and around and around .... Hmm. The kids swing is still in the backyard. I'm very tempted to replace the chains with rods and give it a go .... If my postings should soon stop and never return, then you know why.

But are there other examples not involving gravity, whereby torque can be transmitted to a rotor running on frictionless bearings, such that the rotor can be caused to speed up it's rotation? Without anything touching the rotor except the outer race of the bearings. And of course, no forces from electric or magnetic fields. In other words, is it possible to speed up a spinning (on frictionless bearings) bicycle wheel just by holding and moving the axle? This would appear to impossible, given that torque cannot be transmitted through the bearings to the wheel, and nothing else is permitted to touch the wheel, and forces from all types of field are forbidden. And yet I believe I can build such a device. Any comments?

 

[std_match]

I don't understand your sentence, so don't know if I agree or not. Can you elaborate? And we are all still waiting to know exactly how you would use a (very large) spinning "bicycle wheel" to harness the rotational energy of the earth.

But I do stand by everything that I have said re forces (or torques if you prefer) being at right angles when you change the orientation of the axle of a spinning bicycle wheel. But I might not have made it clear, so will explain in more detail.

Hold the axle of your spinning bike wheel (one hand supporting each end) so that the axle is horizontal. Now, change the orientation of the axle by rotating it in the horizontal plane. A hefty reaction force will be produced, trying to lift one end of the axle, and lower the other end. These vertical forces on the ends of the axle are at right angles to your horizontal movement of the ends of the axle, and therefore you do no work in rotating the axle in the horizontal plane. If you don't believe me, try it. And actually, this must be the case, because if the axle genuinely resisted your altering of it's orientation (rather than producing a force at right angles) then you would be doing work against that resistance. And then physics would be in real trouble. Where would the work done end up? As explained previously, it can't end up increasing the rotational speed of the wheel, because no torque can be transferred through the bearing to the wheel to speed it up.

So, do you agree with what I wrote above?

The "reaction" force is perpendicular to the movement, so no work is done. However, your arms apply a horisontal force, and there is a horisontal movement (the one that creates the reaction force), so your arms are doing some work.
The work ends up as a rotation of yourself and the planet you stand/sit on.

By using a large gyro you can slow down the rotation of the earth and extract that as energy.

 

[Easy peasy]

OK. So grab the pendulum bob, and lift it so that the rod or string is say 30 degrees off vertical. Hold the raised bob perfectly stationary. The angular and linear momentum is zero. Now let it go. It will gain angular momentum

you have created potential angular momentum which is released when the bob is released - this is same as hitting the pendulum/bob - this is not the same as trying to start it from rest ... your logic is faulty again.