Extracting energy from gyroscope precession

[std_match]

If std_match would come on board, then maybe there would be no dissent at all.

I think I now agree with you.

One thought experiment: the spinning bicycle wheel suspended on only one end of the axle (as seen on several videos on Youtube). We agree that the precession force/energy comes from gravity, and the other end of the axle will slowly be lowered.
If you are correct, the unsupported axle end will fall down as if the bicycle wheel wasn't spinning if we block the precession movement without friction.
I was sure that it would still go down slowly, but now I see that everything fits together better if it would go down as fast as a non-spinning wheel. The precession force would be very high.

 

[c_mitra]

One thought experiment:

Compare and contrast a real experiment.

The famous Foucault's pendulum.

The plane of the pendulum can be considered to be the plane of the spinning wheel. For a spinning wheel the angular momentum stays constant but for the pendulum the angular momentum vector changes sinusoidally (but the direction stays in the perpendicular plane).

For the Foucault's pendulum, the length is large, the mass the also large, the friction is very low and the angular momentum is also small.

At the poles, the plane of the pendulum stays the same while the mother earth rotates below. And at the equator, you do not see any effect.

At any other point (not at the pole or not at the equator), you will see the centrifugal force of the earth acting on the pendulum and that will cause the plane of the pendulum to precess. The centrifugal force is now at an angle to the gravitational force.

The precession takes sometime to observe because it is rather slow.

 

[Precision99]

I think I now agree with you.

One thought experiment: the spinning bicycle wheel suspended on only one end of the axle (as seen on several videos on Youtube). We agree that the precession force/energy comes from gravity, and the other end of the axle will slowly be lowered.
If you are correct, the unsupported axle end will fall down as if the bicycle wheel wasn't spinning if we block the precession movement without friction.
I was sure that it would still go down slowly, but now I see that everything fits together better if it would go down as fast as a non-spinning wheel. The precession force would be very high.

Your analysis of your thought experiment is correct. To describe slightly differently, if you hold the spinning wheel in 2 hands and rotate the axle in the horizontal plane, then without a doubt it is observed that the perpendicular reaction torque scales with the speed with which you rotate the axle. And if you don't rotate the axle at all, then the reaction torque is zero. Same in your experiment. No precession rotation means the axle will "fall down"", exactly as you predict. And while it is falling, it will generate a perpendicular torque reaction trying hard to make the axle rotate in the horizontal plane.

I have to admit that the nature of gyroscopic forces are not intuitive. But with sufficient thought, sense can be made of it.

On a related topic, we presumably all agree that with frictionless bearings, it is impossible to speed up or slow down the bicycle wheel by movement or rotation of the axle, because it is impossible to transfer toque through the bearings to the wheel. That was certainly the case in our gyroscope examples, where no work is done when rotating the bicycle wheel axle, and the rotational speed of the wheel remains constant. But I hinted several times that perhaps that may not always be true. What do others think?

 

[Precision99]

On a related topic, we presumably all agree that with frictionless bearings, it is impossible to speed up or slow down the bicycle wheel by movement or rotation of the axle, because it is impossible to transfer torque through the bearings to the wheel. That was certainly the case in our gyroscope examples, where no work is done when rotating the bicycle wheel axle, and the rotational speed of the wheel remains constant. But I hinted several times that perhaps that may not always be true. What do others think?

I can think of two examples. The first example is well known so forgive me if you are familiar with it already. Can the rotational speed and rotational energy of a spinning object increase with no torque applied? Actually, yes.

A spinning ballerina, with arms outstretched, is a rotating wheel on the frictionless bearing of the tip of her foot. No external torque can be applied to her body.

She now brings her outstretched hands and arms in to her body. Her rotational speed, and her rotational energy both increase, despite the fact that no torque has been applied.

I am familiar with the physics behind this, but anyone not familiar may like to think about it.

 

[Easy peasy]

respectfully, a spinning ballerina's rotational energy does not change as she draws her arms in - rotational speed goes up yes - but energy is not gained - your grasp of basic physics is tenuous at best .... time to pick up some 1st year physics texts and read then carefully ....

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Also, Foucault's pendulum if at the poles, rotates or precesses at a maximum speed - contrary to C Mitra above ....

 

[c_mitra]

- rotational speed goes up yes - but energy is not gained - your grasp of basic physics is tenuous at best ...

You are right.

Conservation of energy is a stronger notion in this case.

Rotational speed goes up because the moment of inertia goes down.

Ignoring friction, the angular momentum shall also stay constant.

The spinning ballerina has to exert some internal energy to pull her arms close (a mechanical doll cannot do the same).

Also, Foucault's pendulum if at the poles, rotates or precesses at a maximum speed -

Rotation and precession are NOT the same thing here- rotation is ABOUT the axis and precession is rotation of the AXIS about the direction of the external force.

Due to precession, the Foucault's pendulum will NOT close the orbit (trajectory) after 24 hours (if not at the poles). There is no centrifugal force due to the rotation of the earth at the poles and hence no precession ...

The centrifugal force is strongest at the equator but the direction is along the gravity (away from the centre) and the effect vanishes...

This is also explained in physics texts.

 

[std_match]

Precision99 is correct.
For an outside (stationary) observer, the angular momentum is conservered, not the rotational energy.
By pulling the arms inward, the skater does "work", which ends up as an increase of the rotational energy.

There is a calculation example with a skater a bit down on this page: https://philschatz.com/physics-book/contents/m42182.html

 

[Easy peasy]

I had overlooked work done against the centripetal force forcing the arms and legs out - angular momentum is constant - but not energy - which is supplied by the muscles...

the precession is a maximum at the poles...

 

[Precision99]

Precision99 is correct.
For an outside (stationary) observer, the angular momentum is conservered, not the rotational energy.
By pulling the arms inward, the skater does "work", which ends up as an increase of the rotational energy.

There is a calculation example with a skater a bit down on this page: https://philschatz.com/physics-book/contents/m42182.html

Thank you my friend. As I mentioned in my posting, I am quite familiar with the physics of spinning ballerinas. I have played with them often, or was that swings ...

And I figured that someone else would figure out the truth soon enough.

 

[Easy peasy]

Now you just have to get your head around the swing with no friction is difficult to start from rest ( at bottom ).

 

[Precision99]

Now you just have to get your head around the swing with no friction is difficult to start from rest ( at bottom ).

Perhaps significantly, no one else supports your belief that friction is required to start a swing, plus you have already been wrong on other points, plus you give no reason for your belief, so you don't come across convincingly.

There is no argument that a swing is more difficult to start, if from total rest at the bottom, compared to if you get a small initial movement going using your legs and feet pushing on the ground when you first put your bum on the seat. That is obvious, and not a point of argument.

At first glance, it is not at all obvious that it is even possible to get a swing started from rest at the bottom. But it turns out that it is possible, and friction is not involved. If you think it is, then you need to tell us exactly how this friction is used, and we would also require that practical experience using a swing is consistent with your description of how friction is used.

Unfortunately for you, you have not told us how (in your opinion) friction is used, or why (in your opinion) it is required.

Equally unfortunately for you, actual real-world experience with swings does not provide evidence that friction is used to get the swing moving from rest. And you conveniently neglect the fact that, just as with a pendulum, the friction in a swing is exceedingly small, which should straight away tell you that it unlikely to be a player. And the tiny friction that exists can be further reduced by using thinner ropes or oiling the top "pivot link"in the chain, and this does not make a hoot of difference to the ease which which the swing can be started.

As it happens, I sat in my swing in my back yard just 2 days ago, and specifically experimented with getting the swing started from rest at the bottom, and I can thus report that it is definitely possible and not particularly difficult, plus I saw no evidence that friction was playing any part. And reducing the already tiny friction by oiling the top pivot link in the chain made not a hoot of difference.

I'm really sorry, but when looked at from every angle, the evidence is just not swinging your way.

On all available evidence, friction plays no part in getting a swing started.

 

[BradtheRad]

A similar type of swing has the hero (secret agent 007 as I recall) tied by his hands to the end of a rope suspended over a shark tank. He escapes by gyrating his legs back-and-forth, so that he swings a small distance, growing to a large distance. Finally he reaches a fixture which he clasps with his legs. Resonant action is used to advantage since the swinging is a result of gravity giving back each input of work by his muscles.

Also there is the gymnast who achieves full circles on the high bar. He might start swinging via friction of his hands gripping the bar. Then he gyrates his body to add distance to each swing.

 

[c_mitra]

He escapes by gyrating his legs back-and-forth, so that he swings a small distance, growing to a large distance...

But this effect, not really mysterious, is actually due to air friction. If you have an open umbrella in your hand, it is trivial. It is the same air friction that (mainly) is responsible for the pendulum to stop...

More like a weather vane picks up speed when the air moves.

 

[Precision99]

But this effect, not really mysterious, is actually due to air friction. If you have an open umbrella in your hand, it is trivial. It is the same air friction that (mainly) is responsible for the pendulum to stop...

More like a weather vane picks up speed when the air moves.

Hmmm. Well yes, it is certainly possible to exploit air drag to start (and even pump up) the swinging of a person hanging on a rope. As you say, with an open umbrella this effect could be made very significant.

But you seem to imply that this is the only mechanism, and that it would be impossible to start and amplify the swinging motion without air drag. Is this what you are saying? And do you believe this is also true of a child's swing? Did you read this somewhere on the internet?

Definitely some more discussion required here.

 

[BradtheRad]

Another mystifying real-life demonstration. A heavy disk is mounted on bearings at one end of a bar. When it's spinning a man can easily lift it high in the air by one hand holding the free end.

The key to making it possible is for him to start it precessing as he begins lifting it. So then we wonder if gyroscopic precession is doing the work?

It occurs to ask: Does spinning make the apparatus weigh less? Follow-up video proves the apparatus weighs the same no matter if it's spinning or static.

www.youtube.com/watch?v=tLMpdBjA2SU

 

[Precision99]

Hmmm. Well yes, it is certainly possible to exploit air drag to start (and even pump up) the swinging of a person hanging on a rope. As you say, with an open umbrella this effect could be made very significant.

But you seem to imply that this is the only mechanism, and that it would be impossible to start and amplify the swinging motion without air drag. Is this what you are saying? And do you believe this is also true of a child's swing? Did you read this somewhere on the internet?

Definitely some more discussion required here.

As no one else seems keen to express an opinion (or present evidence) on this, then I'll stick my neck out and say that air drag is most certainly not necessary for starting or pumping up a swing or a person swinging on a rope.

And while it is possible to contrive situations where air drag can be exploited, such as with using an open umbrella, it is my belief that that in normal operation of a swing, any effect from air drag in starting or pumping up the swing is negligible. I base this statement on detailed experimenting and observation using my backyard swing at home, where I found quite clearly that the dominant mechanism is weight shift, not air drag.

Does anyone have a different opinion?

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Another mystifying real-life demonstration. A heavy disk is mounted on bearings at one end of a bar. When it's spinning a man can easily lift it high in the air by one hand holding the free end.

The key to making it possible is for him to start it precessing as he begins lifting it. So then we wonder if gyroscopic precession is doing the work?

I would prefer to say "counterintuitive" rather "mystifying". And certainly fascinating.

I'm not exactly sure what you mean by "wondering if gyroscopic precession is doing the work". What I can tell you is that, ignoring bearing friction, the RPM of the wheel remains constant. Rotational energy of the wheel is never extracted.

However, forcing the precession rotational speed can and does cause a torque reaction in a perpendicular axis. So by forcibly rotating the precession in the vertical axis, as this guy does, it is certainly possible to cause the rotating wheel to lift, and yes, energy that you put into precession in the vertical axis is transferred to lifting the wheel. We already know about this type of energy transfer from previous discussion, where when you support one end of a bicycle axle, it is the drop in the height of the other end of the axle (work done by gravity) that drives the precession about the vertical axis. Conversely, if you forcibly speed up the precession, you will cause the free end of the axle to lift, which is what we see in the video and what you seem to allude to.

All clear and understood? Counterintuitive yes, mystifying no.

Of course the weight of the guy on the ground does not change, except momentarily while mass is being accelerated or decelerated n the vertical direction

 

[Precision99]

As no one else seems keen to express an opinion (or present evidence) on this, then I'll stick my neck out and say that air drag is most certainly not necessary for starting or pumping up a swing or a person swinging on a rope.

And while it is possible to contrive situations where air drag can be exploited, such as with using an open umbrella, it is my belief that that in normal operation of a swing, any effect from air drag in starting or pumping up the swing is negligible. I base this statement on detailed experimenting and observation using my backyard swing at home, where I found quite clearly that the dominant mechanism is weight shift, not air drag.

OK. So in real world experimenting with my swing, I find that air drag is not relevant to starting and pumping up a swing, and that "weight shift" is the dominant mechanism. But that is a woefully imprecise description. I would give no marks for that in a physics exam. To tie this up, I need to explain exactly how "weight shift" is is used to start and pump up the swing. I will now do that.

So exactly how is the swing started, and why does it work? If sitting on a frictionless rotatable office chair, then it is impossible to gain angular momentum (net rotational speed) without an external torque, and you can gyrate and shift your weight all you like, but you will not end up gaining a net rotation. Perhaps this is why c-mitra and easy-peasy (incorrectly as it turns out) said that air drag must be involved. With a swing, it is equally true that you need a torque to get the swinging action started. But in this case, we can generate that torque simply by shifting our weight, and exploiting gravity.

To be precise, all you need to do is to start out sitting in the upright position, and then lean right back, so that your upper body ends up being almost horizontal. This lowers your centre of gravity (COG), but that is not important right now. What it also does is shift your COG backwards. Thus, the line of the chain no longer passes through your COG, and the result is a net torque, acting to rotate your body forward. This is not an inertial effect. You can lean back as slowly as you like, so that inertial effects are negligible. If a second person held the chains to prevent them moving as you leaned back, then after you had leaned back with your body now almost horizontal, he would feel a permanent force (torque) trying to move your body forward.

And so, with no person to resist this newly created torque, your body does indeed start moving forward, and the swing starts swinging.

The physics for this is perfectly sound and, as per the above explanation) not hard to understand. And it actually works. I have done the experiment. Start off sitting upright on the swing, perfectly stationary. Then, lean back, so that your upper body is almost horizontal. It is found that your body starts swinging, back and forth, with a small amplitude. A net torque has been produced, the swinging action is started, and now all that is required is to pump it up.

I'll pause here for comments, and then go on to explain exactly how the swing is "pumped up".

 

[c_mitra]

To be precise, all you need to do is to start out sitting in the upright position, and then lean right back, so that your upper body ends up being almost horizontal.

You are not being honest in your experiments.

If you lean back sitting on a swing so that your centre of gravity shifts outside the seat, you will fall off.

You need to hold on to the ropes to lean back. Then the seat will also move in the opposite way. Note that the seat will move around the point at which you are holding the ropes (or whatever it is supported). The rope above the point you are holding on should stay vertical.

You need to raise your centre of gravity a bit (like what you do when you climb a stairs) and use the gravitational potential energy.

This potential energy need to be transferred to the swing. Loosen your grip on the ropes and bring your centre of gravity back to the seat. You have transferred some energy (equivalent to climbing a height equivalent to the swing vertical rise).

This is all there is in physics.

This lowers your centre of gravity (COG),

Sitting on a stationary swing, raising or lowering the centre of gravity an be performed only on a vertical axis.

What it also does is shift your COG backwards.

If you are not holding on the ropes (holding on the seat is not good enough), you will fall off.

Thus, the line of the chain no longer passes through your COG...

The top part of the rope still stays vertical.

It is a very simple exercise and you need to draw a diagram and see the forces acting at various points.

I agree that it can get confusing sometimes.

 

[Precision99]

You are not being honest in your experiments.

If you lean back sitting on a swing so that your centre of gravity shifts outside the seat, you will fall off.

You need to hold on to the ropes to lean back. Then the seat will also move in the opposite way. Note that the seat will move around the point at which you are holding the ropes (or whatever it is supported). The rope above the point you are holding on should stay vertical.

You need to raise your centre of gravity a bit (like what you do when you climb a stairs) and use the gravitational potential energy.

This potential energy need to be transferred to the swing. Loosen your grip on the ropes and bring your centre of gravity back to the seat. You have transferred some energy (equivalent to climbing a height equivalent to the swing vertical rise).

This is all there is in physics.



Sitting on a stationary swing, raising or lowering the centre of gravity an be performed only on a vertical axis.



If you are not holding on the ropes (holding on the seat is not good enough), you will fall off.



The top part of the rope still stays vertical.

It is a very simple exercise and you need to draw a diagram and see the forces acting at various points.

I agree that it can get confusing sometimes.

You are not being honest in your experiments.

If you lean back sitting on a swing so that your centre of gravity shifts outside the seat, you will fall off.

You need to hold on to the ropes to lean back. Then the seat will also move in the opposite way. Note that the seat will move around the point at which you are holding the ropes (or whatever it is supported). The rope above the point you are holding on should stay vertical.

You need to raise your centre of gravity a bit (like what you do when you climb a stairs) and use the gravitational potential energy.

This potential energy need to be transferred to the swing. Loosen your grip on the ropes and bring your centre of gravity back to the seat. You have transferred some energy (equivalent to climbing a height equivalent to the swing vertical rise).

This is all there is in physics.



Sitting on a stationary swing, raising or lowering the centre of gravity an be performed only on a vertical axis.



If you are not holding on the ropes (holding on the seat is not good enough), you will fall off.



The top part of the rope still stays vertical.

It is a very simple exercise and you need to draw a diagram and see the forces acting at various points.

I agree that it can get confusing sometimes.

Some excellent thoughts there, c-mitra. Your additional details are welcomed. Yes, when you lean back, then of course you need to "hold on" to the ropes. I was well aware of this, but did not mention it.

Starting at rest with no tension in your arms, note that you can raise and lower your COM all you like and you won't get the swinging action started, thus my statement that the key is to shift your COM backwards, which in practice you do by leaning back.

Your statement that the upper part of the chain "will remain vertical" requires explanation. What you really mean is that after you have leaned back and stay leaned back, the new static equilibrium position is with the upper parts of the chain vertical, the lower part of the chain below your hands not vertical, and the line of the upper vertical part of the chain still passes through your COM. Just so, but that is largely irrelevant, because unless you lean back very, very slowly, the system does not gently move to and remain at any such equilibrium. That's the whole point. What actually happens is that you start swinging! The energy to start the swinging has come from gravity.

All I have said is correct. All you need to do is to lean back and stay leaned back, and swinging action is started. No friction required. Do you agree with this?

The subsequent "pumping up" is a separate discussion, and I'll deal with that in due course. And there is definitely some additional physics involved in the pumping up, but let's first agree that by leaning back and staying leaned back, you will start the swing swinging.

 

[asdf44]

No, leaning back should not cause swinging unless there is friction.