Where do the input energy go?

1. Jan 5, 2013

Low-Q

This is an experiment with gyros on a wheel.

First of all, this is not a homework question - I am just a 40 year old man with general interests in physics.

Example: I have a wheel. Attached to its circumference, there are placed heavy discs that is aligned tangentially. These discs are connected to a gear mechanism which will let the discs start spinning fast when the wheel is turned around slowly.

All these discs are now gyros which will resist any change in alignment as they are spinning fast tangentially at the circumference of the wheel.

Initially I must add energy to accelerate the wheel. Now, to maintain a given RPM of the wheel, I must constantly add energy to it, even if friction is not present, because the gyros will try to stop the wheel from turning around.

Where do the input energy go? I ask because in this experiment, I cannot (appearently) get back the energy I add to the wheel except for portions of the energy I added during acceleration. I appearently waste energy that for some reason just disappear. There is no fricton, so there is not generating heat, or other forms of radiation.

Can somebody please explain why it appearently is no conservation of energy in this experiment?

I can make a brief drawing of the experiment if that helps.

Br.

Vidar

2. Jan 5, 2013

Whovian

The gyroscopes, while trying to minimize friction, still allow for some friction, it's physically impossible to engineer such to have no friction. There's also friction with the surrounding air.

So it's going to heat, which, I'm sorry to tell you, once it's gone into the environment, you can't get out without expending significant energy to do so.

3. Jan 5, 2013

Low-Q

Here is the drawing. Reminds me of a power ball when I look at it...

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4. Jan 5, 2013

Low-Q

That was not my point. Read my post again. Conservation of energy, friction etc. is something we all know well about. However, in this thinking experiment there is more than friction that require energy to sustain motion. The gyros will counterforce the rotation of the wheel. Friction will to, but that is not the subject here. This counterforce is made by the gyros, so even if the friction will steal 1Nm of torque, the gyros might steal 100Nm of torque.

So, can you tell me where the energy spent to fight against the gyroscopic counter torque go?

Look at the picture above.

Vidar

5. Jan 5, 2013

Staff: Mentor

If I understand your setup correctly then the work goes into increasing the KE of the gyros.

6. Jan 5, 2013

Low-Q

How can KE increase if the system is stable at one given velocity?

The green circle is part of the gear mechanism that makes the gyros to spin. The gyros must orbit the center of the green circle in order to start spinning. But since the gyros resist disalignment, it will require energy to sustain the cycles at the same rate. It has gained KE by the acceleration of mass, and KE will stay constant until the system slows down. Appearently there has been applied more energy into the system than we in theory can get back when the system slows down to a full stop.

That is what I do not understand.

Vidar

7. Jan 5, 2013

TurtleMeister

Gyroscopes are interesting because they can sometimes be non-intuitive. If you try to rely on your intuition you can possibly be led astray. An example is Eric Laithwaite's famous lecture at the Royal Institution in 1974, where he performed a demonstration and claimed that gyroscopes could be used as a means of reactionless propulsion.

The two gyroscopes in your illustration are rotating in opposite directions. This means that their gyroscopic actions will cancel out (I think this may be where your intuition is leading you astray). If the system is stable at one given velocity then the only energy input required would be for whatever is required to overcome friction.

8. Jan 5, 2013

Low-Q

What if one gyro was spun by the opposite side, so they rotates in the same direction? Or what if one of them was removed?

Other than that, two opposite spinning gyros do not cancel eachother out, they apply eachother. You must see each gyro as separate working units that resist disalignment.

I'm still clueless of where the applied energy goes - energy just can't disappear or be destroied...

Vidar

9. Jan 5, 2013

TurtleMeister

Wrong.

Last edited by a moderator: Sep 25, 2014
10. Jan 5, 2013

Staff: Mentor

This is not correct. It does not require work to sustain the precession. What would make you think that?

11. Jan 5, 2013

the_emi_guy

Vidar,

When gyroscopes "resist any change in alignment" the resistance they offer is perpendicular to the applied force and the motion. In order for the gyroscope to do work, its force must be in the same direction of some motion. Pushing something in a direction that it cannot move does no work, it is like pushing against a wall.

12. Jan 6, 2013

Low-Q

Interesting. Thanks! When the gyroscopes spun in the same direction it looked like a see saw. In my thinking experiment there is no see saw movement allowed. I think I must build it and see for myself :-)

Last edited by a moderator: Sep 25, 2014
13. Jan 6, 2013

Staff: Mentor

Low-Q, energy and angular momentum conservation for isolated systems can be derived directly from Newton's laws. Since this system is governed by Newton's laws we know immediately that those conservation laws hold. However, it is always possible to make a system so complicated that you make a mistake analyzing it. That is why it is best to stick with simple systems. If you ever think you find a violation of some conservation law in a complicated system you know immediately that what you have actually found is a failure in your analysis. Let's walk through the analysis of this device.

There are three important axes, let's call axis A the axis of the toothed rim, axis B is the axis of the two disks, and axis C is the axis perpendicular to both axis A and B. As we apply an external torque about A the toothed gears translates that into two equal and opposite torques about B. Those two torques, being equal and opposite, give equal and opposite angular momentum to each disk. Those two angular momenta cancel out, so the net angular momentum of the device is about axis A. When you remove the external torque, then conservation of momentum demands that the angular momentum (about A) remain.

Now, you wanted to analyze the two disks separately, so let's do that also. Let's call the two disks F and G and let's suppose that the gears are set so that the angular momentum of each points outwards. Let's consider the torques when F is pointing to the right. At that instant the angular momentum of F is also to the right, and since F is precessing towards the back it is experiencing a torque about C (directed towards the back). At that same instant the angular momentum of G is to the left, and since G is precessing towards the front it is experinecing a torque about C (directed towards the front). These two torques cancel and result only in a bending moment in the axis. Assuming a sufficiently rigid and elastic material the net assembly shows none of the deceleration you were suggesting.

14. Jan 6, 2013

Low-Q

Many thanks for the explanation DaleSpam. I suppose I misunderstand the "inner workings" of a gyro. I thought that it was hard (Not impossible) to turn a gyro perpendicular to the rotation plane. I have a bicycle I can test this with. Spinning the frontwheel to high RPM an try to turn the wheel left or right while the bicycle frame remains in the same position. Then I will soon find out if my experiment confirms my thoughts or not.

15. Jan 6, 2013

AlephZero

That seems like a misunderstanding of what happens. It is "easy" to turn a gyro in any direction, but the "non-obvious" behaviour is that it doesn't turn in the same direction as you apply the force, not that it won't turn at all.

16. Jan 6, 2013

Low-Q

My point was however to turn the gyro in the same direction as the applied force - preventing precession using some kind of mechanical guides. That was the attempt to show in the drawing earlier.
Therefor, as the precession is denied, i assumed it would take energy to turn a gyro in the same direction as the applied force, which is prependicular to the rotation plane of the disc/gyro. Such operation I assume will also slow down the gyro, but the toothed rim is forcing the gyros to spin anyways. So I assumed it would recuire energy to do this, and wondered therfor where this applied energy went. However, as you have explained, it will not take energy, so there is no energy that disappears :-)

Vidar

17. Jan 6, 2013

TurtleMeister

I think I understand now what your point is. It was complicated by your illustration, which is not a good example of what you're asking. You mentioned the power ball in one of your previous posts. I think if you read the Wikipedia page and watch the video you will know where the energy goes to (or comes from).

http://en.wikipedia.org/wiki/Gyroscopic_exercise_tool

This is an interesting little gadget. I may have to get one. :)

Last edited by a moderator: Sep 25, 2014
18. Jan 6, 2013

Staff: Mentor

If you want to test the situation in your drawing you will have to get two counter-rotating bicycle wheels mounted on the same axle. That is very different from just one bicycle wheel since one bicycle wheel can be given significant angular momentum, but two counter-rotating bycycle wheels won't have much.

19. Jan 6, 2013

Low-Q

I will use a more simple example.

I have a modified powerball that is fixed to a concrete floor.
Assume that I can turn the flywheel in it perpendicular to the flywheels rotation. Initially the flywheel does not spin. It starts to spin only when I turn it perpendiculary. If I stop turning it, its spin also stop. A gear mechanism makes sure of this.
So, the flywheel will under all circumstances spin in the vertical plane, and at the same time can turn in the horizontal plane - without exceptions.

I assume I will feel a counterforce as soon as I try to turn the flywheel perpendicular to its rotation, since the flywheel at the same time starts to spin perpendicular to the turn. Is that correct?

Say the flywheel is spinning constant at 10 000 rpm. And it turns around perpendiculary at a constant 60 rpm. If I successfully maintan this constant cycle over time, would that also mean that I have to apply energy to sustain the rpm in the vertical and horizontal plane except for making up for friction?

Vidar

20. Jan 6, 2013

Staff: Mentor

Based on the above discussion and your knowledge of physics, what would you guess and why? Think about torque and angular momentum. Think about torque and work. Which torques lead to what changes in angular momentum, and which do work, and why?