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### Author Topic: What is the simplest explanation of gyroscopic precession?  (Read 33661 times)

#### JMLCarter

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##### What is the simplest explanation of gyroscopic precession?
« on: 08/04/2011 00:32:59 »
What is the simplest explanation of gyroscopic precession?

I apply a force perpendicular to the angular momentum and it always gets defected by 90° regardless of the angular momentum magnitude?

I seemed to make some headway by considering twisting stress on a segment of the spinning mass, but I realise I'm not content with my understanding. ( ...and this is classical physics).

« Last Edit: 08/04/2011 00:55:07 by JMLCarter »

#### syhprum

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##### What is the simplest explanation of gyroscopic precession?
« Reply #1 on: 08/04/2011 16:41:31 »
The apparent force that you feel when you move the Gyroscope at right angles to the plane of its rotation is due to the deficiency of the bearings.
With a professional gyroscope with air or magnetic bearings this does not happen.

#### Pikaia

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##### What is the simplest explanation of gyroscopic precession?
« Reply #2 on: 08/04/2011 17:08:38 »
Think in terms of angular momentum vectors.

The initial spin is a vector pointing along the spin axis. If you push down on the top of the gyroscope this imparts a small angular momentum vector horizontally, and at right angles to the axis. Adding these two vectors gives a new vector displaced sideways from the original vector, with the same inclination to the ground.

#### JMLCarter

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##### What is the simplest explanation of gyroscopic precession?
« Reply #3 on: 08/04/2011 21:46:31 »
Precession is not due to inefficient bearings - lol. Are you the sort that tells your kids things like "colour was only invented in 1974".

I have been thinking and I have a submission of my own. Here is the diagram.

When a torque is applied perpendicular to the axis of rotation, a point on the spinning rim experiences opposite forces on opposite sides of the gyroscope (lets say, the back half and the front half). This means that its velocity due to those forces (i.e. neglecting rotation) is greatest half way between the back and the front, i.e. at the sides.

This gives a side-to-side rotation as a result, 90° to the force.

Different assemblies constrain the motion, such as the bottom of the axis being in a stand.

(I didn't expect to answer my own question... first sign of madness   [:-[] )
« Last Edit: 08/04/2011 22:56:33 by JMLCarter »

#### Geezer

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##### What is the simplest explanation of gyroscopic precession?
« Reply #4 on: 09/04/2011 05:09:07 »

Precession is not due to inefficient bearings -

Actually, that's not what Syhprum said, and, I suspect what he did say is entirely correct.

#### moonstroller

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##### What is the simplest explanation of gyroscopic precession?
« Reply #5 on: 09/04/2011 07:41:58 »
Ok, I give up.... what?

Just kidding.

Let me see said the blind man. The axis is the least stable point in this system. It wants to fall due to the effects of gravity. But, then again, the axis acts as a point of support to prevent the force of angular momentum from itself, falling to the ground under the force of gravity so we have a balancing of forces that are happening at the same time.

So, the greater force has to overcome the inclination of the system to give in to gravity and collapse the whole system. The greater force must be associated with the wheel spinning around somehow, and this spinning must be the force that keeps the whole thing balanced. The toy wants to continue to point in one direction after reaching the balance of forces but something else must be pushing it away from this point.... could it be the earth turning, making the toy process? I notice when I try to balance a long stick in my hand, it wants to fall so I have to move my hand to keep it balance and pointing upwards. So.... I went outside and put the stick in my hand and moves my hand around in a circle..... wola.... it was easier to balance the stick once I found the rhythm. So by moving my hand in a circle at a precise rhythm, I was able to do a better job balancing the stick. I think the gyroscope works in a similar fashion. It processes to maintain the balance between the gravitational force, the Axis and the angular momentum of the system spinning around. It should be some form of sum of forces math to describe this.

#### graham.d

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##### What is the simplest explanation of gyroscopic precession?
« Reply #6 on: 09/04/2011 10:56:28 »
Geezer/Syphrum, you seem to agree on something but from what I understood of the question, I tend to agree with JMLCarter. I think there must be some misunderstanding somewhere.

A qualitaitive explanation is as follows:

Take a bicycle wheel and have it spinning in a vertical plane so that the top of the wheel is moving away from you. Now rotate the wheel as though you are steering to the left. The wheel will try to tilt its plane of rotation movong the top to the right and the bottom to the left. You can think of this as trying to change the direction of travel of the mass in the wheel rim at the top from going directly forwards to going at some angle leftwards. The moving mass wants to carry on in a straight line so its momentum resolves itself into a compensating force to the right. The inverse happens at the bottom of the wheel.

Whilst this is not a comprehensive quantitative answer, it does show that there must be a rotational force created at right angles to the applied rotation. I think it helps to understand what's going on and also it enebles you to see what direction the forces work in without trying to remember the signs in equations :-)

I hope this helps.

#### syhprum

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##### What is the simplest explanation of gyroscopic precession?
« Reply #7 on: 09/04/2011 14:40:17 »
JML Carter et al

When you talk of a Gyroscope I take it you have in mind one of those toys you spin up with a string and place one end on a mini Eiffel tower ( If this is incorrect ignore all the following ).
May I suggest that as an experiment that you improve the bearings that are normally steel in brass either by applying some oil or better still some polytetraflouroethelyne (PTFE).
You will find the precessing is much reduced also you could try spinning the rotor in the opposite direction when you will find the precessing direction also reverses.
When a cruise missile comes winging its way overhead pray that it is guided by gyroscopes such as you describe.

PS this also applies to spinning bicycle wheels.

#### JP

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##### What is the simplest explanation of gyroscopic precession?
« Reply #8 on: 09/04/2011 15:27:08 »
Geezer/Syphrum, you seem to agree on something but from what I understood of the question, I tend to agree with JMLCarter. I think there must be some misunderstanding somewhere.

I believe Graham's right.  It's easier to think about this by visualizing a toy top rather than a gyroscope.  A gyroscope brings to mind something with many bearings and axes of rotation which is allowed to rotate freely.  The top is probably what you're thinking of when you put a toy gyroscope on a table so that as it slows down it starts to precess.  Anyway, another way of thinking about the precession of it is angular momentum.  If you want the short version without all the details: spin creates an angular momentum component pointing out the top of the top.  Gravity pulls the top sideways, which creates an angular momentum component at 90 degrees to the spin angular momentum.  Because of how the top works, the only way to add these angular momenta together is for the top's spin axis to tilt in the direction of the gravitational torque, so this axis gets "pulled" at 90 degrees to it's original direction.  This results in precession.

-------------------------------------------------
The longer version with more details follows:

Consider a top spinning counter-clockwise that starts to lean to the left as you look at it.  The counter-clockwise motion tells you that the angular momentum due to spinning is a vector that points out the top of the top (the direction is given by pointing the thumb of your right hand along the top's axis of rotation and curling your fingers in the direction of it's rotation.)

Gravity will tend to create a different rotation, this one about the point of contact between the top and the table.  If the top weren't spinning and you tipped it over, it would rotate about the point of contact with the table as it fell.  You can calculate this effect by computing a torque, which is a vector quantity.  You get it's direction by placing your right with fingers outstretched along the line from the top's point of contact with the table to it's center of mass.  Then you curl your fingers in the direction of the force of gravity (straight down).  Stick your thumb out at 90 degrees and that is the direction of the torque the top experiences.  This torque points forward, towards you, which tells you that the total angular momentum of the top, which was a vector pointing out of the top of the top, has to rotate so it's pointing towards you by a little bit.

Now, because the top's only pivot point is where it contacts the table, and because it already has a lot of angular momentum coming from it's spin, the only way it's total angular momentum can rotate so it's pointing towards you is to tilt forwards slightly.  In other words, the angular momentum is "pulled" forward by a torque acting at 90 degrees to it's original direction.  If you re-do the analysis once it's moved forward a little bit, you'll see the same thing--it always gets "pulled" at 90 degrees to it's axis of rotation.

You might ask why it can't tip sideways instead of forwards.  Well, if it tipped sideways, the total angular momentum, which is mostly due to the spin, would now point more sideways and also forwards.  There is no physical reason for the angular momentum to point sideways, so it doesn't do this.

If all this angular momentum stuff seems odd to you, it's possible to analyze it from Newton's laws, but that requires chopping the top up into tiny pieces and analyzing the forces on each piece.  Angular momentum is basically a very elegant short method to take care of all of this.

#### JMLCarter

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##### What is the simplest explanation of gyroscopic precession?
« Reply #9 on: 09/04/2011 15:56:58 »
Syphrum - how about the precession of the earth on its axis? (I know it seems a bit unkind but I can't resist asking if it needs oiling where it meets the back of the giant tortoise that carries it? "my bad")

Where professional gyroscopes try to minimise precession effects this is by eliminating any torque perpendicular to the axis. They also use improved bearings... ...so that the rotation doesn't get slowed.

#### Geezer

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##### What is the simplest explanation of gyroscopic precession?
« Reply #10 on: 09/04/2011 17:54:33 »
I was just agreeing with Syhprum 'cos he's usually right

#### syhprum

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##### What is the simplest explanation of gyroscopic precession?
« Reply #11 on: 09/04/2011 18:50:11 »
Graham
Let us analyse what is happening, you are sitting holding a non rotating spindle that runs thru the centre of a rotating bicycle wheel which tries to maintain its orientation in space.
when you apply a force to this spindle say to move it in an anti-clockwise direction the friction in the bearing at the front right hand side relative to which the wheel is moving down is increased while the friction at the front left hand side is reduced.
This is where the force that tends to move the wheel at 90° to the direction to which you are moving the spindle is generated.
« Last Edit: 10/04/2011 12:06:01 by syhprum »

#### JP

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##### What is the simplest explanation of gyroscopic precession?
« Reply #12 on: 09/04/2011 19:20:11 »
Syphrum,

Having done a few demos demonstrating precession and the reaction force to changing the axis of rotation, I can tell you that friction doesn't account for it.  Also, I know the theory quite well since I taught it at one point, and Graham's qualitative explanation is right.

By the way, there's a very cool demo you can do with this.  Sit in a rotating chair and hold a spinning bicycle wheel so the axis of rotation is parallel to the floor.  Then try to move the axis of rotation up or down.  Your chair will start rotating in response due to this effect.

#### JMLCarter

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##### What is the simplest explanation of gyroscopic precession?
« Reply #13 on: 09/04/2011 19:21:55 »
friction  [xx(]... ...anyway...

Quote from: JP
If all this angular momentum stuff seems odd to you, it's possible to analyze it from Newton's laws, but that requires chopping the top up into tiny pieces and analyzing the forces on each piece.  Angular momentum is basically a very elegant short method to take care of all of this.

I never liked angular momentum - well, as a tool it is great, but I think the derivation of its properties from "simpler" laws of motion does create a better explanation. (Which I did in the earlier post - how would you do it?).

Perhaps also consider a gyroscope in free space, (such as used to orient satellites). I think it's simpler than the classic toy or spinning top in which one is examining motion that is polluted/constrained by the floor or little tower thing.
« Last Edit: 09/04/2011 20:14:32 by JMLCarter »

#### graham.d

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##### What is the simplest explanation of gyroscopic precession?
« Reply #14 on: 09/04/2011 19:46:42 »
That wasn't a quote from me, JMLC,

#### JMLCarter

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##### What is the simplest explanation of gyroscopic precession?
« Reply #15 on: 09/04/2011 20:16:58 »
Oops it was JP. Darn quote interface - I'll get used to it eventually - sorry.

#### JP

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##### What is the simplest explanation of gyroscopic precession?
« Reply #16 on: 09/04/2011 20:37:43 »
friction  [xx(]... ...anyway...

If all this angular momentum stuff seems odd to you, it's possible to analyze it from Newton's laws, but that requires chopping the top up into tiny pieces and analyzing the forces on each piece.  Angular momentum is basically a very elegant short method to take care of all of this.

I never liked angular momentum - well, as a tool it is great, but I think the derivation of its properties from "simpler" laws of motion does create a better explanation. (Which I did in the earlier post - how would you do it?).

Perhaps also consider a gyroscope in free space, (such as used to orient satellites). I think it's simpler than the classic toy or spinning top in which one is examining motion that is polluted/constrained by the floor or little tower thing.

I think that was my quote.  I'm not sure there's an easy way to get to angular momentum and rotational versions of Newton's laws without doing some work.  Graham was absolutely right.  You can get everything by just looking at small pieces of the wheel and what they do when you try to rotate it's axis.  This is easier to understand, especially if you don't know a lot about angular momentum.  It isn't really a good way of getting quantitative results, since it takes a lot more computation, however.

To really understand angular momentum, you need to understand Newton's laws and work them out for angular coordinates, but the basics of it aren't too hard to understand.  You can describe a rotating object by talking about the angle through which it has rotated, the angular speed with which it rotates, and the angular acceleration, which is the change of angular speed.

If you apply Newton's laws to a rigid object, you get an equation that says that torque equals moment of inertia times angular acceleration.  The only way you cause an angular acceleration, which is a change in angular velocity, is by applying a torque.  In other words, no torque means that angular velocity stays constant..

This is useful because if you define (again for a rigid object) the angular momentum as the moment of inertia times the angular velocity, then the only way the angular momentum can change is if a torque is applied to change the angular velocity.  Also, if you recall from what I said above, all these are vector quantities, so that not only does angular momentum tell you about the speed at which something is rotating, but it also tells you the direction it's rotating about it's axis.  This means that unless a torque is applied, it wants to keep rotating in the same orientation in space with the same angular velocity.

It takes a bit of work, but once you're comfortable with angular momentum, I think it's easier to predict what will happen when you apply torques to a rotating object than by trying to apply Newton's laws to tiny pieces of the rotating object.

#### JMLCarter

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##### What is the simplest explanation of gyroscopic precession?
« Reply #17 on: 10/04/2011 11:47:33 »
JP
I agree with/understand all you have said about angular momentum. But you stopped just short of the bit I find tricky. Which is to "prove/understand" using angular momentum principles that a torque force on the axis results in a fixed angular velocity perpendicular to torque and angular momentum.
Perhaps I need to re-visit vector dot and cross-products.

Anyway at least I understand the effect in terms of little elements of matter on the rim of the gyro. Here's another diagram to complement the first with another view.

« Last Edit: 16/04/2011 00:51:05 by JMLCarter »

#### JP

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##### What is the simplest explanation of gyroscopic precession?
« Reply #18 on: 10/04/2011 14:00:37 »
JP
I agree with/understand all you have said about angular momentum. But you stopped just short of the bit I find tricky. Which is to "prove/understand" using angular momentum principles that a torque force on the axis results in a fixed angular velocity perpendicular to torque and angular momentum.
Perhaps I need to re-visit vector dot and cross-products.

It does take a bit of sitting and thinking about it until it makes sense.  It also takes understanding the angular momentum vectors.  Do you understand why the angular momentum vector due to spin points out the top of the gyroscope, and why the one due to gravity pulling it sideways points at 90 degrees to that?  Once you can understand those points, it's just a matter of knowing how to add vectors, although it still takes a while to puzzle out why it precesses rather than doing some other kind of motion.

The good news is that this is usually subject matter for a first-semester physics course in mechanics.  The bad news is that rotation is one of the toughest parts of such a course, and precession is one of the toughest parts of rotation, so it's definitely very confusing.

But if you don't quite get angular momentum, and you just want to intuit why it moves the way it does without really using numbers, Graham's way is simpler and still correct.

#### syhprum

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##### What is the simplest explanation of gyroscopic precession?
« Reply #19 on: 10/04/2011 16:23:23 »
I thought that the question was how does the force that cause the precession of a rotating disc arise.
My explanation is that it arises in the bearings on the shaft that is used to tilt the rotating disc.
Could anyone please explain how they tilt the disk without using a shaft and bearings as all counter arguments seem to ignore the existence these things.

#### JMLCarter

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##### What is the simplest explanation of gyroscopic precession?
« Reply #20 on: 10/04/2011 18:17:36 »
Do you understand why the angular momentum vector due to spin points out the top of the gyroscope, and why the one due to gravity pulling it sideways points at 90 degrees to that?

Yes I do. It's getting from those two vectors to a velocity vector in the direction of the precession that still seems like a bit of math-magic to me. I don't need angular momentum for understanding (see above) which it seems to make harder, it's just useful to make calculations easier.

Bear in mind that when I did my physics degree it was 20years ago - some of it makes a lot more sense now even though its mostly never been used.

Syph I am asking about fundamental(?) gyroscopic forces, not implementation errors(?) if you like, which I'm sure get really complex; in a sense you may find them a more interesting problem. For this thread I am just asking about the basics - consider about any object spinning in free space to which a torque is then applied along the rotational axis. It will precess.

« Last Edit: 10/04/2011 18:36:07 by JMLCarter »

#### Geezer

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##### What is the simplest explanation of gyroscopic precession?
« Reply #21 on: 10/04/2011 18:38:30 »
I thought that the question was how does the force that cause the precession of a rotating disc arise.
My explanation is that it arises in the bearings on the shaft that is used to tilt the rotating disc.
Could anyone please explain how they tilt the disk without using a shaft and bearings as all counter arguments seem to ignore the existence these things.

I think you are referring to the reaction produced at the bearings (rather than friction) and without good bearings to minimize the friction I think you'd be right in saying that it's not going to work too well.

#### JMLCarter

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##### What is the simplest explanation of gyroscopic precession?
« Reply #22 on: 10/04/2011 18:50:27 »
OK, so the torque force has to be transmitted from its point of application to the rest of the spinning mass.

But that is not special to gyroscopes, even if the mass is not spinning to get it to move the force has to be "transmitted from its point of application to the rest of the mass". (Unless it's force applied equally throughout the mass, like gravity.)

Any more on the vectors? Why is a cross product the right operation to use? I can't see how proof of that can come from angular momentum, it seems necessary to look below at what the angular momentum represents.
« Last Edit: 10/04/2011 19:22:46 by JMLCarter »

#### JP

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##### What is the simplest explanation of gyroscopic precession?
« Reply #23 on: 11/04/2011 04:27:07 »
Any more on the vectors? Why is a cross product the right operation to use? I can't see how proof of that can come from angular momentum, it seems necessary to look below at what the angular momentum represents.

Well, it's used because when you specify rotations, you need to specify the 2d plane in 3D space which the rotation occurs.  Think of a bicycle tire that's positioned somehow in space and spinning.  The easiest way to describe it to me is to say where it is, the way the axle is pointing and whether it's spinning clockwise or counter-clockwise  when you look along the axle in the direction it's pointing.

The most efficient way to describe the axle and sense of rotation is to come up with a standard that everyone agrees upon: the right-hand rule.  You could choose a left-hand rule with equal success, but in order to prevent confusion by having a standard, the right-hand rule is used.

When you use the right hand rule to tell you about angular velocity, for example, clockwise rotation points in one direction and counter-clockwise the opposite.  The orientation of the angular velocity vector in space tells you the object is rotating in a plane perpendicular to that velocity vector.  If you're measuring angular velocity this way, it makes sense to measure angular momentum this way.  This is why it's always given by the right-hand rule.

If it's still confusing, think about a bicycle tire spinning with a constant angular velocity.  Is there a better angular velocity vector that is intuitive (it should also be constant in position and magnitude) and tells you about the wheel's orientation of rotation as well as it's velocity?

Torques can be arrived at by similar intuition.  If you know angular velocity points along the axis of rotation, and you've decided it gets it's sign from the right-hand rule, then you can think about the way applying a force to the wheel changes the angular velocity.  It's obvious that, if the axle is fixed, only a force applied tangential to the wheel's rotation will change it's angular velocity.  Also, intuitively, you would want a torque that speeds up the wheel to point along the direction of the velocity, and one that slows it down to point opposite that direction.  If you enforce these requirements, it's not hard to justify the right-hand rule as giving the torque direction.

This is a somewhat hand-waving explanation.  To get a more quantitative derivation of this, you can follow the same arguments for a mass on a string or some other mass moving in a circle.  The final piece is requiring that angular acceleration be proportional to torque.

#### Geezer

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##### What is the simplest explanation of gyroscopic precession?
« Reply #24 on: 11/04/2011 06:51:19 »
Try this.

Whether a mass is moving or not, it has inertia. It takes a force to alter its inertia.

A rotating flywheel has inertia too, but in this case, the mass happens to be constrained to rotate around an axis. The mass of the flywheel "wants" (for lack of a better term) to remain in the same plane because of a sort of "planar" inertia. Because of this, the axis resists forces that tend to change the direction of the axis.

Therefore, it requires force to alter the plane of the rotating mass, and, in the case of a flywheel, that force has to be applied as a torque that changes the direction of the axis.

After that, its simply a case of resolving the forces associated with producing the torque to see what effect they might have on the supporting structure.

(I've used "inertia" rather than "momentum" here because I think it might help to convey the notion that the flywheel resists forces that tend to change its plane of rotation.)

Feel free to demolish this description. I just made it up!

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##### What is the simplest explanation of gyroscopic precession?
« Reply #24 on: 11/04/2011 06:51:19 »