Extracting energy from gyroscope precession

[Precision99]

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.

Wrong on every count. Go straight to jail. Do not pass GO. Do not collect $200.

(a) There is no such thing as "potential angular momentum".

(b) Releasing an object from rest is most certainly not the same as "hitting" the object.

(c) A pendulum most certainly can be started from rest. And at the instant it is released, it has no angular momentum.

(d) It gains angular momentum as it accelerates towards the bottom of the stroke.

You have utterly failed to answer my question as to where the torque comes from for this angular acceleration, given that nothing physically touches the pendulum to accelerate it, and given that the overhead pivot is frictionless.

The answer is very simple, easy peasy. The force of gravity provides the torque. Provided that the string is not vertical at the bottom of the stroke, the vertical downward force of gravity has a component at right angles to the string, and therefore produces a torque, that in turn produces the angular acceleration. With a simple vector diagram, the component of the gravitational force (mg) that is at right angles to the string is easily shown to be mgSin(theta), where theta is the angle of the string with respect to the vertical.

FYI, for small angles of theta, Sin(theta) is approximately equal to theta, so so for small angles, the restoring torque is approximately proportional to the angle. This (if you can remember your physics) is the condition for producing (angular) Simple Harmonic Motion. And SHM produces a sinusoidal motion, that is, the angular displacement vs time is approximately a sine wave for small amplitudes of oscillation.

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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.

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.

You contradict yourself. First you state "no work is done". Then, in the next sentence you say that "your arms are doing some work"!

I can assure you that no work is done, and that therefore your arms are doing no work. Work is force times displacement, where force is the force (or vector component of a force) in the same direction as the displacement. Therefore, if the force is a right angles to the displacement, as it is in this example, then no work is done, period.

But you still have not told us exactly how you could use a gyro to "slow down the rotation of the earth and extract that as energy." Please explain in detail, using a spinning bicycle wheel for your example. For simplicity, we can assume that the experimental is carried out at the N or S pole. Is the plane of the spinning bicycle wheel horizontal or vertical? I'm guessing vertical, though you have never told us.

And then what? It's not good enough to blandly state that "By using a large gyro you can slow down the rotation of the earth and extract that as energy." You need to give us the details as to how you would actually do it.

 

[Easy peasy]

(d) It gains angular momentum as it accelerates towards the bottom of the stroke.

You have utterly failed to answer my question as to where the torque comes from for this angular acceleration, given that nothing physically touches the pendulum to accelerate it, and given that the overhead pivot is frictionless.

Sigh, the potential energy of the lifted bob - gravity accelerates the bob to the bottom - imparting angular momentum from the potential it was at previously - and giving it kinetic energy also...

So work was done by lifting the bob - and then released into the system when the bob is released - no different from hitting the bob to the same height

failure to see this simple fact is also a factor in failure to see the difficulties in starting a swing in a frictionless environment ...

 

[Precision99]

Sigh, the potential energy of the lifted bob - gravity accelerates the bob to the bottom - imparting angular momentum from the potential it was at previously - and giving it kinetic energy also...

So work was done by lifting the bob - and then released into the system when the bob is released - no different from hitting the bob to the same height

failure to see this simple fact is also a factor in failure to see the difficulties in starting a swing in a frictionless environment ...

The pendulum bob could have started out at any height. It could just as well have been stored in the attic, and then attached to the string or rod, with the rod at the top of the stroke, and then lowered to the starting position. So forget about "lifting" or "hitting" the bob prior to it being released - that is all arbitrary and irrelevant. The only thing that matters is that the height of the bob decreases after the bob is released, and that therefore gravity does work on the bob. But that does not explain how torque is exerted on the pendulum, which in turn causes angular acceleration resulting in increasing angular momentum, and saying in a vague way that the angular momentum is "imparted" to the bob is not an explanation. You would get zero marks for that in a physics exam. But never mind. I explained how the torque is produced precisely and thoroughly in my previous posting, so you can read that if you want to know.

I will leave others to decide, based on previous postings, whether friction is required to start and pump up a swing. It isn't. Again I urge you to find a swing and experiment with it, and see if increasing the friction in the top pivot makes it easier to start and pump up. The explanation of how a swing is started and pumped up has already been given, but you have not explained why (in your opinion) friction is required to start a swing, or exactly how friction is used and exploited to start a swing. Please give us the explanation.

And, in case you missed it in previous postings, your previous argument that the swing's angular momentum starts at zero (true), and that therefore friction is the only mechanism by which torque and angular momentum can be imparted to the swing, turns out not to be valid for swings, where changes in height and gravitation potential energy can be exploited, although it is valid for a rotating office chair. You got a lot of 'splaining to do with your belief that swings rely on friction ...

 

[Nik_2213]

Came a bit late to thread but, IMHO, OP's query is akin to the rocket fallacy, 'In space, what does it push against ?'

If you attach a crank to the top bearing of a slanted gyroscope, so precession winds crank, does work, then the gyroscope RPM gotta slow to provide it.
'Owt for nowt.'

Mechanically, you're looking at something akin to a swash-plate engine, see...
http://www.douglas-self.com/MUSEUM/museum.htm
... but prepare to lose yourself to awe & wonder...

Also, with apologies to several posters, bearings 'bear'. Magnetic, air, sleeve, ball, roller or needle, even recirculating, a bearing is still a bearing.
N

 

[Precision99]

Came a bit late to thread but, IMHO, OP's query is akin to the rocket fallacy, 'In space, what does it push against ?'

If you attach a crank to the top bearing of a slanted gyroscope, so precession winds crank, does work, then the gyroscope RPM gotta slow to provide it.
'Owt for nowt.'

Mechanically, you're looking at something akin to a swash-plate engine, see...
http://www.douglas-self.com/MUSEUM/museum.htm
... but prepare to lose yourself to awe & wonder...

Also, with apologies to several posters, bearings 'bear'. Magnetic, air, sleeve, ball, roller or needle, even recirculating, a bearing is still a bearing.
N

Welcome to the madhouse.

But I must disagree with you. Firstly, gyroscopes have nothing in common with a swashplate. A swashplate is in effect a kind of crank, so no mystery about how how torque is transmitted to the swashplate and thus swashplate shaft.

But a gyroscope, or a bicycle wheel with bearings between the axle and the wheel, are not constructed like a swashplate or crankshaft. You say that gyroscope rotor (or spinning bicycle wheel) "gotta slow down" if you attempt to extract energy from the precession. Nope. That is not possible because of the bearings, which prevent torque being transmitted from shaft to rotor. And to the extent that real bearings do have a small amount of friction, that will act to slow down the rotor or bicycle wheel, not speed it up. Your thoughts need to go "back to the drawing board".

 

[std_match]

You contradict yourself. First you state "no work is done". Then, in the next sentence you say that "your arms are doing some work"!

I can assure you that no work is done, and that therefore your arms are doing no work. Work is force times displacement, where force is the force (or vector component of a force) in the same direction as the displacement. Therefore, if the force is a right angles to the displacement, as it is in this example, then no work is done, period.

There are two forces involved. One from your arms and one as a reaction from the gyro. The simplest case is when we keep the gyro (bicycle wheel) spinning axis horizontal during the movement. The reaction force from the gyro is then perpendicular to the movement, so no work is done. The force from your arms is not perpendicular to the movement, so work is done. It may not be obvious where this work is going, but it isn't stored in the gyro. We agree that the gyro will not spin up or down due to external forces if we ignore bearing friction. You are not a fix point in space, so the work goes to a change in the movement of yourself and ultimately to a small change in the movement of the earth.

 

[Nik_2213]

I'm sorry, P99 but, IMHO, as soon as you connect any constraining mechanism to the precessing axle, and begin to extract work from system via that precession, the dynamics are totally changed.

Never mind 'perfect' bearings: If supplying that work does not 'draw down' on the gyro's flywheel spin, it's a 'perpetual motion' machine.

Sorry, as I said in my first post, akin to 'rocket' fallacy.

 

[std_match]

I'm sorry, P99 but, IMHO, as soon as you connect any constraining mechanism to the precessing axle, and begin to extract work from system via that precession, the dynamics are totally changed.

Never mind 'perfect' bearings: If supplying that work does not 'draw down' on the gyro's flywheel spin, it's a 'perpetual motion' machine.

Sorry, as I said in my first post, akin to 'rocket' fallacy.

An external force is needed for the precessing force to exist. If you only support one end of a gyroscope, the external force is the gravity. In that case, any energy extracted from the precessing comes from gravity and the loss of potential energy (the unsupported end of the gyroscope will move closer to ground). The spinning RPM of the flywheel in the gyroscope is not affected.

 

[Precision99]

An external force is needed for the precessing force to exist. If you only support one end of a gyroscope, the external force is the gravity. In that case, any energy extracted from the precessing comes from gravity and the loss of potential energy (the unsupported end of the gyroscope will move closer to ground). The spinning RPM of the flywheel in the gyroscope is not affected.

Exactly correct. You pointed this out many postings back, but evidently that got lost in the noise.

But let me add some further detail. If you brake the precession rotation only slightly, so that precession continues at a constant speed, then that's the end of the matter. You can continue to extract energy by braking the precesssion, for as long as the centre of gravity of the spinning wheel is able to drop, which is of course limited.

But if you decelerate the precession rotation, then you can extract a little bit more energy. That is because there is rotational energy stored in the precession rotation, which can be extracted if you slow down the precession. The wheel has 2 moments of inertia, one about the (relatively high speed) rotation of the wheel on it's bearings, and a numerically different moment of inertia about the precession axis of rotation. In both cases, the stored rotational kinetic energy is 0.5Iw^2, with different I and w for the main rotation and the precession rotation. The 2 stored rotational kinetic energies are independent. When you slow down the precession rotational speed, then you extract energy from the speed of precession, but not from the rotational speed of the wheel on it's bearings. As most would know, I is the moment of inertia, and w is the rotational speed in radians per second.

That, I believe, completely ties up the original question posed at the start of this thread. But there are a few questions that popped up along the way that still require resolution. But they too will be resolved. That is the beauty of science.

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There are two forces involved. One from your arms and one as a reaction from the gyro. The simplest case is when we keep the gyro (bicycle wheel) spinning axis horizontal during the movement. The reaction force from the gyro is then perpendicular to the movement, so no work is done. The force from your arms is not perpendicular to the movement, so work is done. It may not be obvious where this work is going, but it isn't stored in the gyro. We agree that the gyro will not spin up or down due to external forces if we ignore bearing friction. You are not a fix point in space, so the work goes to a change in the movement of yourself and ultimately to a small change in the movement of the earth.

OK. Let's resolve this. If you are holding the spinning bicycle wheel, then all forces are provided by your arms. Your body and your muscles do no work at all when you rotate the axle in the horizontal plane. Period.

So your argument is apparently that as the wheel produces a torque reaction as you rotate the axle in the horizontal plane, then that torque reaction is transmitted to mother earth, and thus (incredibly slightly) alters the rotation of the earth, and that in thus doing, an (incredibly small) amount of energy is transferred to the earth. Well sure, of course that is true, but I make the following comments.

This effect occurs every time we move or accelerate anything at all, but the effect is so small that we never talk about it or consider it, and rightly so. When I get in my car and accelerate to 100 km/hr, do I need to take into consideration that I have altered the earth's rotation? Of course not. And as soon as I start my car engine, even before moving the car, then I alter the earth's rotation by virtue of the angular acceleration of the crankshaft and flywheel when the engine is started. And when I get up in the morning, I slow down the earth's rotation because my moment of inertia is greater when standing than lying down. Life would descend into chaos if we considered all these countless billions of totally insignificant effects, so you can understand why your claims that work was being done on the earth had me puzzled for so long. The torque reaction generated by the spinning wheel and transferred to the earth is of course significant and easily measurable, but the energy thus transferred to the earth is so close to zero that we would be best to ignore it.

One might be tempted to think that if you rotated the spinning bike wheel axle in the horizontal plane for long enough, then the cumulative effect of the torque reaction on the earth would eventually become significant. But it turns out this is not true. The torque that you transmit to the earth by a constant rotation of the axle in the horizontal plane is oscillatory, and thus averages to zero over multiple rotations. Another reason to ignore it.

But you and I still need to resolve your claim that a large spinning "bicycle wheel" could be used to harness usable energy from the earth's rotation. This definitely needs to be resolved, but first you need to tell me exactly how you intend to do it.

 

[std_match]

OK. Let's resolve this. If you are holding the spinning bicycle wheel, then all forces are provided by your arms. Your body and your muscles do no work at all when you rotate the axle in the horizontal plane. Period.

No. If something moves in the direction you apply force, work is done. If you resist the tilting of the spinning axis or in some other way prevent the tilting, the only movement will be the "axle rotation in the horizontal plane", and since that movement is done by the force from your arms, work is done. The precession force from the gyro tries to tilt the spinning axis and does no work if you prevent the tilting.

Imagine yourself in free space with a spinning gyro. Apply force (torque only if you don't want the gyro to move away) to change the spinning axis of the gyro and let go of it. The gyro will stay in the new spinning axis and you will rotate in the opposite direction of the torque you applied. Compared to the start you are now spinning. Did that require some work or not?

 

[Precision99]

No. If something moves in the direction you apply force, work is done. If you resist the tilting of the spinning axis or in some other way prevent the tilting, the only movement will be the "axle rotation in the horizontal plane",and since that movement is done by the force from your arms, work is done. The preces sion force from the gyro tries to tilt the spinning axis and does no work if you prevent the tilting.

Imagine yourself in free space with a spinning gyro. Apply force (torque only if you don't want the gyro to move away) to change the spinning axis of the gyro and let go of it. The gyro will stay in the new spinning axis and you will rotate in the opposite direction of the torque you applied. Compared to the start you are now spinning. Did that require some work or not?

Chatting with you is a pleasure, as we both have a good knowledge of physics, and I find you postings coherent and logical.

But in this particular case, I'm honestly not sure what the argument is. Maybe we are cross purposes, actually agreeing with each other, but because of some misunderstanding we think we disagree.

(a) If something moves in the direction you apply force, work is done. Correct.

(b) If you resist the tilting of the spinning axis or in some other way prevent the tilting, the only movement will be the "axle rotation in the horizontal plane",... Correct

(c) ... and since that movement is done by the force from your arms, work is done. No! The movement of your hands is at right angles to the vertical reaction force, and thus no work is done. There is no component of torque or force in the direction of movement of your hands, is there?

(d) The precession force from the gyro tries to tilt the spinning axis and does no work if you prevent the tilting. Correct.

Your (c) is in plain contradiction to (a), (b) and (c).

Imagine yourself in free space with a spinning gyro. Apply force (torque only if you don't want the gyro to move away) to change the spinning axis of the gyro and let go of it. The gyro will stay in the new spinning axis and you will rotate in the opposite direction of the torque you applied. Compared to the start you are now spinning. Did that require some work or not?

Of course that required work, because in this case you are not able to hold the rotation of the axle in a horizontal plane. In this case, there is a torque and a rotation from your hands that are in the same direction, and so in this case of course you do work. But that is irrelevant to the discussion. Back here on earth, we are discussing a quite different situation where the experimenter keeps the precession rotation of the axle in the horizontal plane, because he has the essentially infinite mass of the earth that allows him to do so, and thus no work is done.

Why on earth (if you will pardon the pun) are we apparently disagreeing on such a basic point of physics?

And we still need to know how you are going to harness energy from the earth's rotation using a large rotating "bicycle" wheel. (Or by any other means)

 

[std_match]

Back here on earth, we are discussing a quite different situation where the experimenter keeps the precession rotation of the axle in the horizontal plane, because he has the essentially infinite mass of the earth that allows him to do so, and thus no work is done.

You mean that the spinning axis will change without the hands applying any force/torque in the direction of the change? That 100% of the force/torque from the hands will be used to resist the precession force? That is not the case.
The precession force is a consequence of a movement created by an external force, This means that the net movement can never be 100% in-line with the precession force. Some work must be done (by the external force).

The discussion is directly related to the possibility of extracting energy from the earth's rotation. A gyroscope on earth with the spinning axis perpendicular to the earth axis will appear to rotate one turn every 24 hours.
Resisting that rotation is equivalent to changing the spinning axis of the bicycle wheel, and we disagree about whether "work" is involved or not.

 

[Precision99]

You mean that the spinning axis will change without the hands applying any force/torque in the direction of the change? That 100% of the force/torque from the hands will be used to resist the precession force? That is not the case.
The precession force is a consequence of a movement created by an external force, This means that the net movement can never be 100% in-line with the precession force. Some work must be done (by the external force).

The discussion is directly related to the possibility of extracting energy from the earth's rotation. A gyroscope on earth with the spinning axis perpendicular to the earth axis will appear to rotate one turn every 24 hours.
Resisting that rotation is equivalent to changing the spinning axis of the bicycle wheel, and we disagree about whether "work" is involved or not.

So let us summarise the physical setup, just to be sure there is no misunderstanding. We carry out the experiment on earth, and the earth's mass is effectively infinite.The spinning bicycle wheel axle is held horizontal, with one hand under each end. Of course, our hands are supporting the weight of the wheel, but that is not relevant to the discussion. We then use our hands to rotate the axle in the horizontal plane. While thus being rotated, our hands must counteract an upward force on one hand, and a downward force on the other. But that is all.

You mean that the spinning axis will change without the hands applying any force/torque in the direction of the change? Yes. Absolutely.

That 100% of the force/torque from the hands will be used to resist the precession force? Yes. That is the case.

Not only is that the case, it necessarily must be the case. Because if you were right and work was done by your muscles in rotating the axle as discussed, then you would have to explain where that energy has gone to, and you cannot, because we agree that there is no increase in the rotational speed of the wheel on it's bearings. Unless and until you can explain where your claimed work from the human muscles has ended up, then you are necessarily wrong.


The precession force is a consequence of a movement created by an external force (strictly speaking, a rotation of the axle in the horizontal plane)

First, allow me to re-word your sentence more precisely :-

The vertical forces at the ends of the axle, which strictly speaking is a torque, is a consequence of the rotation of the axle in the horizontal plane.

This means that the net movement can never be 100% in-line with the precession force.

Again. Allow me to be more precise. When you rotate the axle in the horizontal plane, then the axis of that rotation is vertical, while the axis of the reaction torque produced is horizontal. Thus, no work is done in rotating the axle in the horizontal plane as per our experiment. You will need to get used to that fact. Take a spinning bicycle wheel and try it, as I have done, and you will observe that all I have said is true. But in any event, what I have said must be true for conservation of energy.


The discussion is directly related to the possibility of extracting energy from the earth's rotation.

A gyroscope on earth with the spinning axis perpendicular to the earth axis will appear to rotate one turn every 24 hours. Correct.

Resisting that rotation is equivalent to changing the spinning axis of the bicycle wheel, and we disagree about whether "work" is involved or not.

So let's first be clear about the mechanical setup. You have a frictionless generator, and you anchor the casing of the generator to mother earth, with the generator shaft vertical. You then attach the bicycle wheel axle to the end of the generator shaft, with the bicycle wheel axle horizontal. And you would claim that if you attach an electrical load to the generator, then the spinning bike wheel on it's axle will turn the generator, and produce electricity. I don't care if the electrical power produced is very small - this is a thought experiment, and I'm only interested in fundamental concepts, not practicality. And small though the electrical power produced might be, you could do this continuously, right?

Sadly this won't work. You see, if this did work, then the torque exerted on the earth would slow down the rotation of the earth. The angular momentum of the isolated system that is the earth and the bicycle wheel must remain constant. So if you are steadily slowing down the rotation of the earth, decreasing it's angular momentum, then you must be steadily increasing the angular momentum of the bicycle wheel by an equal amount. Really? I don't think so. Can you explain how that could happen? When the requirement for conservation of angular momentum of the (earth + spinning-wheel-gyro-thing) is considered, I think you will find it very difficult to extract energy from the earth's rotation. Do you still think your idea would work?

 

[std_match]

Ok, now we know in detail why we don't agree.

Your argumentation is in the reverse order:
Since the energy can't go anywhere, no work is done, and therefore the force must be zero.

My argumentation is different:
A force is needed to move anything, work is done, in this case the energy is stored as an acceleration/deceleration of the earth's rotation.

There is no meaning to discuss harvesting energy from the earth's rotation as long as we disagree about this.

 

[Precision99]

Ok, now we know in detail why we don't agree.

Your argumentation is in the reverse order:
Since the energy can't go anywhere, no work is done, and therefore the force must be zero.

My argumentation is different:
A force is needed to move anything, work is done, in this case the energy is stored as an acceleration/deceleration of the earth's rotation.

There is no meaning to discuss harvesting energy from the earth's rotation as long as we disagree about this.

I am telling you how I think the forces (or actually torques) on a spinning wheels work, and noting that my explanation is consistent with conservation of energy and angular momentum. You can't ask for better that that.

You are telling us how you think the forces (or actually the torques) on a spinning wheel work, and I point out that your explanation cannot be correct, because your explanation violates conservation of energy and angular momentum. So which explanation/description is more likely to be correct? And what you say in your posting is not correct, as explained below.

A force is needed to move anything No. In linear mechanics, a force is required to acccelerate a mass, not to move it. And in angular mechanics, a torque is required to produce angular acceleration.

... in this case the energy is stored as an acceleration/deceleration of the earth's rotation.

I'm not sure exactly which case you refer to, your earth energy harvesting, or an experimenter rotating the axle of a bicycle in the horizontal plane as we discusssed. But you are wrong in either case.
In my explanation, everything adds up, and there are no violations of energy or momentum conservation, as must be the case.

If you rotate the axle of a spinning spinning bicycle in the horizontal plane, then a perpendicular reaction torque must be provided by your hands. This is the torque that is responsible for the change in angular momentum, as you rotate the axle. It may seem counterintuitive that the reaction force is perpendicular to your rotation of the axle, but trust me, that is the case.

Here is a simpler example that is rather similar, and may make you feel more comfortable about what is gong on. Consider circular motion. The speed and kinetic energy are constant, and there is a constant acceleration towards the centre of rotation. The force required to provide this acceleration is always at right angles to the motion, so no work is done constraining an object to move in circular motion. Presumably you don't have a problem with that?

If what I say is right, then your claim that energy can be extracted from the earth's rotation using a spinning wheel must also be wrong, and it is. Let's just say that your idea was correct, and that you really could use a spinning wheel as a "rotational anchor". You say that when you rotate the axle of a spinning bicycle wheel in a horizontal plane, then a torque about a vertical axis is produced. If this was the case, then rotational kinetic energy would be imparted to both the wheel and the earth, just as surely as if you throw a ball in the air, kinetic energy is imparted to both the ball and the earth. If you do the simple math with the ball example, you find that the energy imparted to the earth is negligible because of the almost infinite mass of the earth, and I'm happy to provide the math is if you doubt that is true. The same holds for rotation. If you have a wheel on a vertical axis, and you speed up the rotation of the wheel by applying a torque, then the exact equal and opposite torque is applied to the earth, and the earth therefore also changes it's speed slightly, and gains energy. But as with the linear case, if you do the math, you find that the energy imparted to the earth is negligible because the earth has a far greater moment of inertia compared to your wheel, and can be ignored. Again, I can provide the math for this.

Returning to your (incorrect) claim re rotating the axle of a spinning bike wheel in the horizontal plane. You claim that an opposing torque is produced about a vertical axis. If this was true, then kinetic energy would be imparted to the wheel and the earth, because torque reactions are always equal and opposite. But that is not we observe. The kinetic energy of the wheel does not increase, though it angular momentum is forced to change. And even if your contention was true, the increase in kinetic energy of the earth would be negligible. Like I said, I can show the math for that.

The only description that correctly describes what we observe, and that correctly predicts conservation of energy and angular momentum, is the one one I have given. That is, when you rotate the bike axle in the horizontal plane, the torque reaction is entirely at right angles, forcing one end of the axle down and the other up. Rather than flogging a dead horse, you would be better to consider that what I tell you might actually be true, and take an attitude like, "hmm, I didn't realise that, that's actually quite interesting, and all the physics does work out perfectly with that explanation ..." Just a suggestion. I am happy to continue the discussion, because there is only one correct answer, so eventually we have to agree. That is the beauty of science. Unsubstantiated opinions don't count, and conservation of energy and momentum must not be violated. It is not a matter of your opinion versus mine. The problem with your description is that it does not match what we observe, and energy and angular momentum are not conserved, and therefore your description must be wrong.

 

[Precision99]

Ok, now we know in detail why we don't agree.

Your argumentation is in the reverse order:
Since the energy can't go anywhere, no work is done, and therefore the force must be zero.

My argumentation is different:
A force is needed to move anything, work is done, in this case the energy is stored as an acceleration/deceleration of the earth's rotation.

There is no meaning to discuss harvesting energy from the earth's rotation as long as we disagree about this.

I never make a claim that I can't back up. In my last posting, I claimed that when there is an equal and opposite reaction force or torque, as there always is, then the energy that is imparted to the two bodies is not equal, and that the larger body will receive less kinetic energy. Of course, both bodies receive and equal and opposite amount of momentum, as required to conserve the momentum of the total system.

Re the transfer of energy to the two bodies, it turns out that the amount of energy imparted to the bodies is in inverse proportion to their mass. So, as the mass of the earth is very large indeed, the energy imparted to the earth from a reaction force or torque will be exceedingly small,and can be neglected. Let's state that mathematically, and then I'll prove it.

SMALLER BODY
mass = m
moment of inertia = i
imparted linear velocity = v
imparted angular velocity = w
imparted energy = e

LARGER BODY
mass = M
moment of inertia = I
imparted linear velocity = W
imparted angular velocity = W
imparted energy = E


For simplicity, I will from here on speak only of the linear case, but the angular case works in exactly the same way.
As stated, whenever you apply a net force (or torque) to an object, by accelerating a body, then there is always an equal and opposite reaction force produced on the earth. As a result, you impart velocity and energy to both the object and the earth. But it turns out that the energy imparted to the earth is negligible small because the mass of the earth is incredibly large. Mathematically, the result is :-

E = em/M

So if you believe the above result, then the energy imparted to the larger mass is smaller by the ratio (m/M). And as that ratio is so close to zero that it does not matter, we can neglect the energy imparted to the earth in all practical situations. Including, of course, in the proposed method of harnessing energy from the earths rotation. But I don't ask you to take me on trust on anything, so here is the derivation of this expression.

As discussed, the force imparted to the two objects is always equal, and so too is the time for which the separating force is applied. For simplicity, we will assume that both objects start from rest. So you apply a force that separates the 2 objects, and they fly apart. This is the linear equivalent of applying a torque between the 2 objects - one will rotate in one direction and the other will rotate in the other direction. But, as stated, I will only specifically discuss the linear case for simplicity.

OK. So you exert a separating force F for a time t.

Both objects will thus accelerate :-

a = F/m
A = F/M

As a result of these accelerations, over the common time t, both objects will experience a change in velocity :-

v=at = Ft/m
V=At = Ft/M

OK. as a result of the changes in velocity, each now has a kinetic energy :-

e = 0.5mv^2
E = 0.5MV^2

Substituting in the expressions for the velocities, we get

e = 0.5m F^2 t^2 / m
E = 0.5M F^2 t^2 / M

Dividing these gives :-

E/e = m/M

Or if you prefer :-

E = em/M

Which is exactly what I wrote at the start of this posting, which is now shown to be correct. QED


The math is identical for rotation. In that case, the result is :-

E = e i/I

And as the moment of inertia of the earth is incredibly large, we can completely neglect any energy imparted to the earth by applying a net torque to the earth. Thus, for all practical purposes, all of the rotational energy expended by the torque ends up being transferred to the smaller object, as per the ratio (i/I)

And so we find, as I stated previously, that your various claims cannot be right, because you have an issue with energy conservation. With all of the experiments we have discussed, any work done cannot end up increasing (or decreasing) the kinetic energy of the earth, as you claimed, because the ratio (i/I) is effectively zero. And on top of that, you are in trouble with conservation of momentum, as previously explained.

I conclude, as a matter of demonstrated fact, not opinion, that your claims are wrong, and that my description is correct. Are you convinced?

 

[Precision99]

Ok, now we know in detail why we don't agree.

Your argumentation is in the reverse order:
Since the energy can't go anywhere, no work is done, and therefore the force must be zero.

My argumentation is different:
A force is needed to move anything, work is done, in this case the energy is stored as an acceleration/deceleration of the earth's rotation.

There is no meaning to discuss harvesting energy from the earth's rotation as long as we disagree about this.

I have done to death the reasons why your particular scheme for harnessing energy from the earth's rotation cannot work. But by applying only the principle of conservation of angular momentum, we can confidently conclude that any proposed, earth-bound method of harnessing the earths rotational energy must fail. That is the power of physics. If you understand and trust the over-arching principle of conservation of angular momentum, then you don't even need to know the details of someone's energy-harvesting idea to confidently say it cannot work. It's like if someone claims to have invented a machine that outputs more energy than it consumes. You don't need to know the details of the proposed machine to state confidently that it cannot work.

OK. The reasoning goes like this. The angular momentum of any isolated system is a constant, and cannot change. If you were to really slow down the earth's rotation, then you would need to speed up the rotation of something else so that the total angular momentum remained constant. That is, of course, very possible and it happens every time you start something spinning, be it a bicycle wheel or your car engine. But here is the unfortunate crunch. No such scheme can operate to constantly thus extract rotational energy from the earth and slow it's rotation, because if it did, then something else would need to gain angular momentum indefinitely, and that is impossible. It really is that simple.

I can tell you details of many schemes that have been devised for extracting energy from the earth's rotation, and many such ideas are far more subtle than your suggested spinning wheel idea. But I don't need to know how each idea is claimed to work, in order to confidently know and state that they will not and cannot work.

But star-man Joe or moon-girl Sally can extract energy from the earth's rotation, because in that case it is possible to exchange angular momentum between the star or the moon, and earth, and this actually happens by way of the tides created by the gravitational pull of the moon. But alas, any earth-bound machine or idea to extract energy from the earth's rotation will fail. Always.

So how about extracting energy from the precession of the earth's axis of rotation? Is that possible? Are those gyro exerciser balls good for something after all.

 

[c_mitra]

So how about extracting energy from the precession of the earth's axis of rotation? Is that possible? Are those gyro exerciser balls good for something after all

Things can be confusing but I am not here to add more.

In Cartesian space, you have motion on a straight line, kinetic energy is (1/2)m.v^2. This v is nothing but dx/dt.

Lagrange made lots of simplifications to the Newton's laws of motion. If we use a polar coordinate set for our measurements, dr/dt is similar to velocity but d(theta)/dt is angular velocity.

If r is constant (just assume for the time being), the kinetic energy is (1/2)I*w^2 where I has taken over m and omega has taken over from v. How?

Lagrange introduced the concepts of generalized coordinates and generalized momenta. In this case the generalized coordinate is theta and the generalized momentum is I*w

I see lots of confusion because you are going from Cartesian and polar coordinates without respect for the proper transformations. The transformation is provided by the Jacobian (it is not really that messy)

Precession of the earth's axis is rather small (think about 25000 years? a few degrees) but it is theoretically possible to extract energy from this precession.

Just like the precession of the top is caused by the gravitational field (yes, torque is the analog of force in polar coordinate), the precession of the earth's axis is caused by perturbations of other planets. Fortunately these are also periodic forces and it is not difficult to study these effects.

Just like the tides in the seas cause a friction slow down the rotation of the earth.

But alas, any earth-bound machine or idea to extract energy from the earth's rotation will fail. Always.

You can harvest the energy in the tides and that works. As you extract this energy, the angular momentum of the earth-moon system is converted into some useful energy (which was otherwise dissipated as heat). The result will be slowing down of both earth and moon.

Again, I repeat, this would not have been possible if earth were a rigid body.

 

[Precision99]

Things can be confusing but I am not here to add more.

In Cartesian space, you have motion on a straight line, kinetic energy is (1/2)m.v^2. This v is nothing but dx/dt.

Lagrange made lots of simplifications to the Newton's laws of motion. If we use a polar coordinate set for our measurements, dr/dt is similar to velocity but d(theta)/dt is angular velocity.

If r is constant (just assume for the time being), the kinetic energy is (1/2)I*w^2 where I has taken over m and omega has taken over from v. How?

Lagrange introduced the concepts of generalized coordinates and generalized momenta. In this case the generalized coordinate is theta and the generalized momentum is I*w

I see lots of confusion because you are going from Cartesian and polar coordinates without respect for the proper transformations. The transformation is provided by the Jacobian (it is not really that messy)

Precession of the earth's axis is rather small (think about 25000 years? a few degrees) but it is theoretically possible to extract energy from this precession.

Just like the precession of the top is caused by the gravitational field (yes, torque is the analog of force in polar coordinate), the precession of the earth's axis is caused by perturbations of other planets. Fortunately these are also periodic forces and it is not difficult to study these effects.

Just like the tides in the seas cause a friction slow down the rotation of the earth.



You can harvest the energy in the tides and that works. As you extract this energy, the angular momentum of the earth-moon system is converted into some useful energy (which was otherwise dissipated as heat). The result will be slowing down of both earth and moon.

Again, I repeat, this would not have been possible if earth were a rigid body.

All completely agreed, and not inconsistent with anything I have said previously. And yes, you can harvest energy from the tides, but only because an external mass (moon) is involved. When I said that Sally moon-girl could extract energy from the earth's rotation, that was intended to include harvesting energy from tides, which are as a result of the gravitational interaction between moon and earth.

And yes, at least in principle, you can extract energy from the earth's precession which, like the tides, is as a result of gravitational interaction with external masses. Pity about the 25,000 year period though.

I would be surprised if we disagreed on anything in this thread. If std_match would come on board, then maybe there would be no dissent at all.

 

[c_mitra]

And yes, at least in principle, you can extract energy from the earth's precession which, like the tides, is as a result of gravitational interaction with external masses. Pity about the 25,000 year period though.

This page http://hosting.astro.cornell.edu/academics/courses/astro201/earth_precess.htm says that the precession period is about 26000 years.

Yes, you are right when you invoke external gravitational forces- they are producing the field. Without external fields, precession is not possible. It has to be external to the spinning top.

Solar or wind energy comes from the heat radiated by the sun (which is a kind of nuclear energy by the way but a bit far away).

Tidal energy is on the other hand essentially gravitational in nature. Because of coupling of the spin and orbital angular momenta, moon is slowly going away from us (but it may take some time and noting to worry for the time being).

A spinning top in a field-free space cannot show precession (or nutation for that matter).

An isolated system is conservative by definition- and by isolated system I mean a system free from external influences. Both angular momentum and total energy are constants of motion.