Bicycle wheel on the North Pole

[petermarrick]

Hi You'all, Newbie here so no calculus or polysyllabics on the first date please.

If I hold a bicycle wheel horizontally and spin it at the north pole, the torque from the Earth spinning and the torque from the bicycle wheel are along the same axis.

Does this mean the wheel could float off into space if the torques repel, that is if my wheel spins in the opposite direction to the Earth which is spinning west to east?

Obviously not but how do the 2 torques from the right hand rule interact based on the wheel spinning east - west or west east? Would the weight of the wheel vary up or down depending on which way it was spinning? Does the Earth actually precess northwards a microscopic amount every year? Is my wheel likely to precess under the torque of the moon or the sun?

If I had the same wheel at a location 45° longitude, would I have to spin it so the axle faced north south and the wheel inclined 45° to the horizontal to achieve the same result?

Is there likely to be a 'sweet spot' less than or greater than 45° where the angular momentum keeping the wheel in place is able to counteract the forces of gravity pulling it downwards as with a spinning top?

An answer to any of these questions or a pointer to a good book on the subject is appreciated!

 

[CWatters]

Does this mean the wheel could float off into space if the torques repel, that is if my wheel spins in the opposite direction to the Earth which is spinning west to east?

No.

Would the weight of the wheel vary up or down depending on which way it was spinning?

No. You cannot make a reactionless engine using flywheels.

Imagine a horizontal axle with a wheel (a flywheel) on each end. If you rotate the axle about the mid point the whole axle does not get lighter. It just bends.

 

[Simon Bridge]

Welcome to PF;

Hi You'all, Newbie here so no calculus or polysyllabics on the first date please.

OK, but it will get dull...

If I hold a bicycle wheel horizontally and spin it at the north pole, the torque from the Earth spinning and the torque from the bicycle wheel are along the same axis.

Does this mean the wheel could float off into space if the torques repel, that is if my wheel spins in the opposite direction to the Earth which is spinning west to east?

No.

Obviously not

Indeed.

but how do the 2 torques from the right hand rule interact based on the wheel spinning east - west or west east? Would the weight of the wheel vary up or down depending on which way it was spinning?

No.

I've met engineers who thought that torque or angular momentum could be used to generate lift.
All it does is turn stuff.

When you hold your wheel horizontal at the "north pole", you see it does not turn because you are turning with it. Spin it so it rotates once a day against the spin of the Earth and you have canceled out the spin imparted by the Earth. But once you'd stopped pushing it, there will be no torque, and, in the absence of friction, it should stay like that as long as you are prepared to hold it there.

Does the Earth actually precess northwards a microscopic amount every year? Is my wheel likely to precess under the torque of the moon or the sun?

Torques are pseudovectors ... to work out how forces combine to make an object move you have to add up the forces - some of them will make objects precess etc.

But to "precess" the motion is perpendicular to the pole direction.
Are you thinking that maybe the Earth's spin makes the plane of it's orbit shift?

If I had the same wheel at a location 45° longitude, would I have to spin it so the axle faced north south and the wheel inclined 45° to the horizontal to achieve the same result?

Same result as what?

Is there likely to be a 'sweet spot' less than or greater than 45° where the angular momentum keeping the wheel in place is able to counteract the forces of gravity pulling it downwards as with a spinning top?

No. To stop the wheel, as with the top, from falling, you have to put something under it.

I think you need to work through the classical physics of a rotating reference frame ... oh, I promised no polysyllabics... hmmmm... you need to read about stuff that goes on because the whole world turns.

You should also review what "precession" means and how it happens.

 

[jbriggs444]

Torques do not repel. There is no levitation effect. A spinning bicycle wheel, a motionless bicycle wheel, a bicycle wheel spinning backwards, a bicycle wheel spinning horizontally, a bicycle wheel spinning vertically. They all fall to the ground at the same speed. They all take the same amount of force to hold up.

One case where you can get what might look like a levitation effect is when you hold an upright, spinning bicycle wheel by one end of its axle and observe that it remains upright even though there is nothing holding up the other end of the axle. If you try this, the bicycle wheel will precess in a circle. The faster it is spinning, the slower the precession will be.

The catch is that the support force that you need to exert on the one end of the axle to hold up the wheel is equal to the weight of the bicycle wheel. If you held it up on both ends, you'd be supporting half the weight at each end. Either way the total required support force is equal to the weight of the wheel.

 

[CWatters]

and easily demonstrated by climbing onto some weighing scales.

 

[petermarrick]

Thanx for the replies..

OK, so levitation is out, no escaping the scales of injustice, question is, will there be any untoward force on the bearings. I'm holding it horizontal so I expect thrust at the base to counter gravity but in a perfect world I imagine I would have no horizontal pressure on the bearings, even with the Earth rotating below me.

At the 45° longitude location, I would expect some pressure at the cylindrical bearings around the axle and a thrust bearing at the base to repel gravity, what I am hoping to avoid is any pressure on the bearings due to torque/s acting on the wheel from the Earth's gravity which is why I have it on the incline and align the axis..

 

[CWatters]

Standing on the pole with the wheel horizontal and the axle vertical... all you have are vertical loads on the bearings due to the weight of the wheel. There is no precession or anything like that going on.

At the 45° longitude location, I would expect some pressure at the cylindrical bearings around the axle and a thrust bearing at the base to repel gravity...

Correct. The Earth's rotation east/west causes the gyro to precess north/south. The load on the "thrust bearing" (aka the weighing scales) is unchanged.

.. what I am hoping to avoid is any pressure on the bearings due to torque/s acting on the wheel from the Earth's gravity which is why I have it on the incline and align the axis..

Ok so now you have lost me. You are saying that you are at some latitude (say 45 north) and with the axis of the gyro inclined (not pointing to the centre of the earth) and aligned with something?

Diagram please.

 

[russ_watters]

Why are you saying there are torques applied here? I'm not seeing any.

 

[CWatters]

Is there likely to be a 'sweet spot' less than or greater than 45° where the angular momentum keeping the wheel in place is able to counteract the forces of gravity pulling it downwards as with a spinning top?

Ah I think I see what you are suggesting. Basically you are asking...

Does the fact that the Earth's rotation is precessing the wheel allow the axis of the wheel to lean over slightly without the top end appearing to precess in a circle to a local observer?

I believe it does.

However it will still weigh the same as measured on scales under the whole aparatus.

 

[physwizard]

If I had the same wheel at a location 45° longitude, would I have to spin it so the axle faced north south and the wheel inclined 45° to the horizontal to achieve the same result?

To add to the rest of the comments, it would be the latitude which has an impact on the centrifugal force due to the Earth's rotation, and not the longitude. At the poles the longitude will become many valued.

 

[physwizard]

Torques are pseudovectors ...

Why do you say this?

 

[Simon Bridge]

Torques are pseudovectors ...

Why do you say this?

Because it may be (off post #1) core to OPs misunderstanding - thinking of a torque as producing a thrust in the direction of the "arrow" and wondering how different torques may combine or transform.
http://en.wikipedia.org/wiki/Pseudovector

Waiting for OP to return and provide feedback before elaborating further.

 

[physwizard]

Because it may be (off post #1) core to OPs misunderstanding - thinking of a torque as producing a thrust in the direction of the "arrow" and wondering how different torques may combine or transform.
http://en.wikipedia.org/wiki/Pseudovector

Waiting for OP to return and provide feedback before elaborating further.

Interesting!

 

[petermarrick]

Thanks again, if only for forcing me to clarify what it is I don't know that I don't know.

Apart from my longitudes and latitudes, I have a basic query.

So we've established that a horizontal spinning bicycle wheel with its axis extending from the Earths' axis has only its weight to support by a thrust bearing to oppose the force of gravity.

Similarly a bicycle wheel at the equator spinning vertically and parallel to the equator with its axis parallel to the Earths' axis (north - south) should have only gravity acting on it and can be supported with a standard bearing either side of the axle to oppose the force of gravity.

Although if I remove one hand and support only the other side of the axle, the wheel then maintains the axle in the horizontal plane but precesses in a circular fashion about the supporting point which suggests there is a horizontal force at play on the bearings prior to the hand being removed.

Anyway, the confusing part is midway between the poles and the equator where in order to minimise precession and keep the axle parallel with the Earth's axis I have to tilt the wheel away from vertical. Then the effects of gravity create a huge incentive for the wheel to begin precession. But if I keep the wheel vertical then the Earth's rotation invites the wheel to precess.

Is there any hiding from precession? Is there an achievable happy medium or is the majority of the population doomed to precessing bicycle wheels? Is this why the most productive flywheels look like hot water systems?

I am hoping your answers will not involve the hodge dual or pseudoscalars as I have no idea where they live.

 

[CWatters]

Similarly a bicycle wheel at the equator spinning vertically and parallel to the equator with its axis parallel to the Earths' axis (north - south) should have only gravity acting on it and can be supported with a standard bearing either side of the axle to oppose the force of gravity.

Correct.

However if you spin it with the axis locally vertical it will be precessed by the Earth's rotation - so it should try to rotate slowly in the north<>south direction. However see below..

Anyway, the confusing part is midway between the poles and the equator where in order to minimise precession and keep the axle parallel with the Earth's axis I have to tilt the wheel away from vertical.

That's two different things.

1) minimise precession

The Earth's rotation is very slow. It's effect on the giro is likely to be very small.

2) keep the axle parallel with the Earth's axis

That's a different thing. At 45 degree latitude if you want the axis parallel to the Earth's it's going to have to lean 45 degrees. If supported there will be bearing side loads due to gravity. If not supported it will precess around due to gravity and that will mask any small precession effect due to the Earth's rotation.

 

[jbriggs444]

First, realize that the effect that you are trying to resist is trivial. It amounts to a precession rate of approximately one rotation in 24 hours.

Position yourself on the equator with the bicycle wheel held horizontally. So its axis points directly at the center of the earth. Hold your hands steady and attempt to keep the axis vertical as the Earth spins beneath your feet.

Let us assume that you are facing east. And let us assume that the bicycle wheel is spinning clockwise as viewed from the top.

As you rotate through a small angle, your hands will begin to impose a torque on the axle. This torque acts in the direction of rotation of the earth. You will be pushing forward/east on the top of the axle and backwards/west on the bottom.

In response to this torque the bicycle wheel will try to precess. The top end of the axle will tend to move southward. The bottom end of the axle will tend to move northward. This is the right hand rule in action.

[Personally, I can never keep the right hand rule memorized. So I just think of which direction of precession would result in the rotation aligning more closely with the applied torque over time]

But remember that you are trying to hold the axle steady in place. You will resist this attempted precession by pushing northward on the top of the axle and southward on the bottom.

This resistance will tend to cause its own precession. The top of the axle will tend to move eastward and the bottom of the axle will tend to move westward.

*Voila* -- this is exactly the motion that you need in order to keep the axle vertical as the Earth under your feet rotates eastward.

In steady state, if you close your eyes and hold your hands steady, the top of the axle will be precessing eastward at the correct rate as a result of the north/south forces that you are continuously applying. The east/west force that you started to apply will go away.

But again, the required forces are trivial. You are not likely to even notice them.