# Gyroscope question

1. Jun 8, 2007

### B.E.M

Suppose we have two wheels connected along the same axis, spinning in opposite directions. (zero sum angular momentum) The whole contraption is welded inside a box. Could someone handling the box tell any difference between if the wheels were spinning or not?

2. Jun 8, 2007

### AlephZero

There would not be any large-scale effects that could be felt from outside.

This idea is used with contra-rotating aircraft propellors, and contra rotating shafts in jet engines, to reduce gyroscopic effects.

(Contra rotation has some aerodynamic advantages in those situations, as well.)

3. Jun 8, 2007

### Splinter-Cat

i don't think that's correct aleph.

gyroscopic force is applied when a spinning wheel's axis changes angle, in the direction resisting the applied force. i believe that if you have two wheels spinnng at angular velocities v and -v, they will apply the same gyroscopic force as eachother.

correct me if i'm wrong, but i think that two wheels spinning in opposite directions on the same axis (and rotating about the same origin) will produce the same gyro force as two wheels spinning in the same direction.

4. Jun 8, 2007

### pervect

Staff Emeritus
No, the forces will be in opposite directions. Aleph's analysis in terms of total angular momentum is the easiest way to see this.

Note that this assumes that the connecting shaft is perfectly rigid. There can be very large torques on this shaft with the proposed conditions. Under these conditions the connecting shaft may flex (or if it is improperly designed, it could even fail). There would probably be some observable effects if the shaft were not perfectly rigid (there would be obvious noticable effects if the shaft failed!), but I'm not sure what they would be offhand.

5. Jun 8, 2007

### rewebster

It would just depend on how long the axis is. If it was short, you couldn't probably tell. If the axis was long, you could lift one end of the 'box' and move it. You'd get a reaction of an angular displacement.

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It seems to me that if the box was moved in any direction, other than where the axis and the diameters of the discs remained in the same plane, there would be some 'reaction' at 90 degrees in both discs (therefore 'some' movement --90 + 270---the box would 'twist') of the box that you wouldn't normally get, if the discs weren't rotating.

Last edited: Jun 9, 2007
6. Jun 8, 2007

### Langbein

Will a shaft with two gyros really be neutral with no "gysoscopic effect" (= will not be balancing like a gyro) ?

One thing is for sure, when rotor a that rotates CW is pushed forward at the upper shaft it will tilt to the right. When rotor B is rotating the other way it will try to tilt the other way (Due to the cariolis effect.)

But I have allways beleved that a shaft with two rotating masses that rotate the oposite way, still will have the "gyroscopic rigidty" so the shaft should still be able to balance on its end. Possibly I'm wrong ?

Last edited: Jun 8, 2007
7. Jun 8, 2007

### Langbein

I know that for a socaled "gyroscopic platform" there are used two gyroes to stabilize the platform, but those gyros might not be on the same shaft ?

(Gyro platforms is used in inertial navigation systems and in gyro compasses I believe.)
http://en.wikipedia.org/wiki/Inertial_guidance_system

8. Jun 8, 2007

### Langbein

9. Jun 15, 2007

### B.E.M

Interesting (re the gyro platform)

In what manner does a gyro platform resist twisting? Would it feel like a drag, seeking to always slow the twisting, or an inertia, so it is hard to begin twisting but then equally hard to stop?

Re the contra rotating propellers, wouldnt this mainly be to prevent such problems as a constant twisting of the plane opposing the direction of the propeller and a more violent twist if you suddenly increase thrust?

I was wondering if the two wheels could exibit higher angular inertia. This isnt specifically excluded just because they have no total angular momentum. For example consider two weights connected by a shaft. Increasing the shaft length would increase the inertia and has nothing to do with angular momentum.

Nevertheless I am of the opinion that they simply cancel as AlephZero suggests, ie that a single gyroscope produces no resisting force, only the sideways deflecting force, so two wheels simply cancel... But im still dont know how I would set about absolutely proving it.

10. Dec 10, 2007

### Syd12107

Done the experiment ...

Hi all,

I've done the experiment with two lecture gyroscopes each spinning at about 10K rpm mounted on the same axis:

Spinning in opposite directions -> no gyroscopic stabilization (acts just as if the gyroscopes were not spinning, ie., the gyroscopes fall over exactly as when they are not spinning - zero net angular momentum)

Spinning in the same direction -> double gyroscopic stabilization (twice the angular momentum, so twice the stabilization)

If anyone is interested, I can include a jpeg of them (assuming I can figure out how to upload the jpeg).

Just thought you might wish to know the experimental results,
Syd

11. Dec 10, 2007

### wysard

My off the cuff answer was that given a hypothetically rigid system (perfectly rigid axis, no slop etc.) that you could not tell the difference.

Then I thought about it for a second and realized that I think you could still tell. Follow my process and correct me where I went astray.

Given the box with the gyros is perfectly cubic and there is no way to tell what the orientation of the gyros are, nor whether they are spinning or stationary.

We will use a simple test and use some hypothetical strain gauges where our hands are.

1) hold the box in front of you.
2) holding the left hand stationary, rotate the right hand in a circle in the "zy" plane (relative to you holding the box) and measure the strain at the left end and right end and record.
3) turn the box 90 degrees in the z plane and repeat 2
4) turn the box 90 degrees in the y plane and repeat 2

If all readings are the same, the gyros are not turning (or perhaps don't exist)

If the gyros are turning, then in 2 of the 3 tests the strains cancel out or balance making an effective zero. But on 1 of the 3 the gyros are situated such that they are mounted vertically on a horizontal shaft between your two hands. In that position when you rotate the one end of the box in a large circle, where the other hand just wobbles ( assuming the sides of the cube are rigid) then the deflection of one gyro, while of the same angle net to zero, is the same as the other, it's magnitude is not and will cause a net "kick" at right angles into one hand or the other. (Try spinning a bicycle wheel and then twisting it in a rapid circle with some "x" deflection to see what I mean). This will not only tell you if the gyro is spinning, but give you some idea as to the nature of the properties of the hidden gyros themselves.

12. Dec 12, 2007

### Syd12107

Double gyros...

Hi wysard,

Basically, let's assume the mechanical setup is ideal, that is, it is perfectly balanced with perfect frictionless bearings and infinitely rigid support and axle rod. Thus when the double gyro is rotated, even though each gyro by itself will place a perpendicular stress upon its bearings, those bearings are perfect and thus there is no vibration stimulated. The connecting axle is also infinitely rigid, and thus does not bend under stress but conveys the forces as if it were a rigid body. I also assume that there are no Special Relativity effects, such as $$E=mc^2$$ effects. In other words, when the gyros are being spun up, we add energy to them and thus according to $$m=E/c^2$$ they are slightly more massive than when the gyros are not spinning. If we neglect these effects, then I believe that since the net angular momentum is zero the gyros's axle can be moved in any direction about its central pivot point by any applied force without experiencing a 90 degree precessional motion, that is, a motion directed 90 degrees from the direction of the applied force.

In the schematic drawing, the downward applied force (solid cyan arrow) would normally result in the horizontal precession (dashed cyan arrow) if only the front (red) gyro were spinning. But with the back (green) gyro spinning in the opposite direction, the same downward force at the front would produce an upward force (darker solid cyan arrow) because of the pivot point (blue) that would normally result in the horizontal precession (darker dashed cyan arrow) if only the back (green) gyro were spinning. Assuming perfect balance and exactly opposite angular momenta, these two precessions will exactly cancel each other. The same is true for the magenta forces and their 90 degree precessions -- they too will exactly cancel in a perfect idealized setup. Notice that the cyan forces are in the vertical plane while the magenta forces are in the horizontal plane (these are thus two of the three possible directions that the axle can be pushed). The only other direction that you can push the axle is along its axis, and a force along the axis does not produce a torque since the lever arm's radius is zero (or, in other words, the cross product of the angular velocity and the pushing force is zero). Pushing along the axle thus does not produce any torque and would only produce an acceleration of the center of mass of the system (and a difference between spinning and nonspinning gyros would only be detected by an increase in mass, $$m=E/c^2$$, of the spinning gyros). Since any force applied to the axle can be decomposed into a linear combination of horizontal, vertical, and axial components, and the horizontal and vertical components produce canceling precessional motions, then, neglecting effects from Special Relativity, the double counterrotating gyros behave the same whether they are spinning or not.

As I mentioned in my first post (ever), I tried this with two lecture gyros. Now they aren't mechanically perfect, the axle isn't infinitely rigid, the bearing aren't frictionless, and it is difficult to spin them up to roughly 10K rpm and have them have exactly the same magnitudes (but opposite sign) of angular momentum. Nevertheless, I think you might be pleasantly surprised how the precessional motion vanishes when you perform the experiment. So, please have a look at the photograph of the setup - the two gyros are mounted on an axle, and the axle is suspended in a mount that allows free motion both in the vertical plane (up-down movement) as well as in the horizontal plane (rotation about a vertical axis). When one gyro is spun up, the pair behaves (obviously) just like it should if there were only one gyro --- you apply a force in one direction and the response is a precession at a 90 degree angle to the applied force (normal gyroscopic reaction, in other words). But after spinning up the second gyro in the opposite direction, then any force applied pushes the axle in the direction of the force, just as if neither gyro were spinning. When I actually perform these experiments, it is amazing how accurately the behavior of the oppositely spinning gyros repeats the behavior of the nonspinning gyros. In other words, pushing the axle with my finger behaves the same whether the gyros are not spinning or whether they are counterrotating. My only problem is getting them to spin at the same rate and thus have the same magnitudes (but opposite directions) of angular momentum. Since the spin up is accomplished by a small motor temporarily attached to the end of the gyros's axles, I have to quickly spin one up and then the other before the first one slows too much. But the gyros will spin unaided for over ten minutes on their own, so this allows me to get them fairly close in angular velocity and thus angular momentum. Any slight disparity in angular momentum (ie, slight nonzero net angular momentum) is masked by the friction in the pivot mount, thus I really do not visually observe any precession when I applying a force along any direction to the spinning double gyros.

In summary, I can push the axle of the nonspinning gyros and the unit responds by moving in the direction of my finger push. I can also push the axle of the counterrotating spinning gyros and the unit responds by moving in the direction of my finger push - same as the nonspinning case. If only one gyro is spinning and the other is not spinning, then pushing on the axle produces a motion at 90 degrees to the direction of my finger push (gyro precession, in other words). If both gyros are spinning in the same direction, then pushing on the axle produces a 90 degree motion (precession) but with a lower frequency (due to the higher angular momentum). If we allow Special Relativity effects, then the energy $$\Delta E = (1/2)I\omega^2$$ it takes to spin up the gyros makes them more massive via $$\Delta m=\Delta E/c^2$$, and this additional mass, albeit quite small, could in theory be measured.

Regards,
Syd

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Last edited: Dec 12, 2007
13. Jan 1, 2008

### szuminga

gyroscopic torque

NO! if two high speed wheels spinning in the opposite direction in an enclosed box, the gyroscopic torques will be canceled b/c of the opposite spinning wheels and therefore know one could tell if the wheels were spinning or not.

14. Jun 25, 2009

### Pebble

My thinking is that there would be resistance to any torque applied perpendicular to the axis of rotation.
If torque is applied to a single gyro spinning one way then resistance is felt.
If torque is applied in the same direction as above to the single gyro spinning the opposite way then resistance is still felt.
Therefore torque applied to the double gyro system in question must produce resistance. Probably double, assuming a very short distance between gyros.
Precession would however be canceled out.

15. May 28, 2011

### twilliam.gage

I have to admit that I would have suspected the same effect as what Pebble describes - but the experimental evidence submitted by Syd12107 would appear to contradict what I suspected.
If I understand the description of the experimental results, then not only is the precession "canceled," then resistance to change in orientation was also canceled. Which is completely unexpected for me!
I must assume that I have an incomplete understanding of angular momentum / inertia. It would seem from this that the sum of the angular momentum of the two gyroscopes becomes zero for the system - thus canceling any stabilizing effect of the spinning masses.
However, two factors lead me believe that I will have to do some experimentation for myself to clarify this.
First - Syd12107's description seemed to focus on the absence of the precession effect, although it did seem to imply in the broader meaning of the cancelling of all stabilizing effects.
Second - the military helicopters using the countra-rotating blades should seem to suffer from a serious problem in stability, resulting from the loss of total angular momentum. Although, my knowledge of the designs used is close to nil - so perhaps there are additional measures used to retain the stability while still benefiting from the countra-rotation.

Syd12107 - can you confirm that you did mean that the stabilizing effect was also "cancelled," not just the precession effect?

16. May 29, 2011

### Quinzio

His post dates back to 2007, so probably, Sid is probably "not on the other side of the phone" anymore.

I can confirm you that two gyros connected with a rigid system that are counter rotating shows no gyroscopic effect.
No precession, no stabilization. It reacts with its mere mass as a still object.

17. May 29, 2011

### pallidin

I'll surely have to try this sometime.
My intuition says one thing, but reality might well be different.

18. May 31, 2011

### Pebble

I don’t think Syd’s experiment contradicts my comments. My comment is based on there being little to no distance between the gyroscopes.
Syd’s experiment has the gyroscopes a significant distance apart (compared to their size). This will lessen the peculiar behaviour of the gyroscopes we all know and love.

Considering a gyroscope’s resistance to rotation and precession come from it being rotated about the centre of it's axis, Syd’s experiment has the gyroscopes rotating about the midpoint between the two gyros (travelling in an arc). Therefore the centre of the axis of each gyro is travelling and rotating about the circumference of a circle where the centre is the middle of the two gyros (a much slower rate than if rotated about the gyro's centre). Being that gyros are all about momentum and momentum is affected by acceleration, the key point is that the rate of change in rotation about the centre of the gyro’s axis is much less in Syd’s experiment than if they were positioned very very close together.

This being the case I think there would be resistance to the rotation of the twin gyros in the experiment only it was too small to register. I believe this is shown in the occurance of precession in one of the cases.

Something else to note is that when Syd says the gyros are rotating in opposite directions I suspect, due to the fact that they are on opposite sides of the centre of rotation, that they are actually spinning the same way. eg rotate one of the gyros 180deg around the middle to sit on top of the other. It is spinning the same way.

Last edited: May 31, 2011
19. Dec 29, 2011

### oddino

If one displaced the "spin axis" a few degrees off of horizontal would it hold the new angle or return to horizontal? It would seem both spinning masses would retain their inertial orientation.

Jim O

20. Mar 27, 2012

### Pebble

It would hold the new angle. Even though there is resistance when turning a gyroscope, when you remove the force there is no 'bounce back'.