PDA

View Full Version : Explaining precession simply but accurately

grant hutchison
2005-Oct-17, 04:09 PM
May I pick some brains here?
I'm writing about precession (of the Earth, and then eventually of the Moon's orbital plane) for a general audience who will be interested in science, but most likely quite vague about detail - in particular, they're not necessarily going to be familiar with angular momentum, and are likely to know nothing about vector algebra. But I want, if possible, to give them a sense of why a rotating gyroscope does this counterintuitive thing of moving at 90 degrees to the applied force.
Here's where I'm at, and I'd really like some feedback to let me know if it's horribly misleading, and if it's misleading if there's anything I can do to fix it.

1) If a big heavy thing is going past you in a straight line, and you give it a shove, it doesn't move off in the direction of the shove: instead, you deviate its course slightly in the direction of the shove.

2) The flywheel of a vertical, spinning gyroscope can be thought of as a train of heavy things moving past you: the rim nearest you is moving (say) left to right, and the far rim is moving right to left.

3) So give the top end of the gyroscope axis a poke, briefly - try to tilt the gyroscope away from you. That poke, once it's transmitted to the flywheel, is in effect an upward shove on the near rim, and a downward shove on the far rim. So (following on from our everyday experience in 1) above), the near rim now is moving left to right and slightly upwards; the far rim, right to left and slightly downwards.

4) The only way the solid body of the flywheel can accommodate these two deflections is by tilting leftwards, at right angles to your poke. QED.

Of course, it rather draws a veil over what the other parts of the flywheel are doing during this experiment, but it seems to be a way of thinking that moves the behaviour of a gyroscope from "Huh?" to "Yeah, OK."

Grant Hutchison

Ken G
2005-Oct-17, 04:54 PM
Well I think that's a wonderful explanation, I learned something from it myself! My only suggestion is you might want to get rid of the poking the axis concept altogether, and go straight to pushing up and down on the near and far sides. I realize you wanted to avoid the image of friction, so you'll just have to say to do it frictionlessly, like with very slippery hands. This will serve you better when you get to the Earth's precession. You are golden as long as the idea emerges that when external forces try to tilt the axis of rotation a certain way by pushing up and down on the sides, it ends up going at a right angle to what you might expect.

Incidentally, there is an alternative take you might consider, which is like adding angular momentum vectors but doesn't really require vector concepts.
First imagine that the gyro is not spinning at all, and ask what axis of spin you would generate by the action you describe. The axis would be sideways. Now go back to the spinning case, and note that you should not interpret the rotation axis itself as a physical object you can push around. It is the gyro that is the object, and if you try to give it one axis of rotation and it already has another, it will end up with a combination of the two, i.e., the one axis will tilt down toward the other axis you are trying to create.
This bridges the gap between non-spinning and rapidly-spinning gyros, and makes the point that a rotation axis is not a physical thing (i.e., the axis that a sphere wants to rotate around is not necessarily the same as the direction of the rod you've drilled though it). But I see advantages to your way as well, since it relates linear motion concepts to rotation in a very elegant way.

Maybe you could offer both explanations and let either stick in their minds, or pick the one you like better. You obviously have a good feel for how to make subtle concepts understandable.

grant hutchison
2005-Oct-18, 11:27 AM
Well, that's been an easier ride than I expected (so far).

Many thanks for the kind words and comments, Ken G.
I know what you mean about the axis thing. But I guess I'm hoping the occasional person will get an old toy gyro out of the cupboard, fire it up, and poke it. So I'm trying to keep this real-world doable, while agreeing it involves another step in the logic which I could have eliminated. (Otherwise I'll need a disclaimer that goes: "The author accepts no liability for damage, injury or death resulting from attempts to follow these instructions.")

The vectors-by-stealth argument is good. But I do find people sometimes get in a conceptual fankle trying to see that the intrinsic rotation of a spinning body and the externally imposed tilting caused by the poke of a finger are examples of the same thing. They feel they're somehow being tricked into combining apples and oranges, and resist the idea.
I get the famous argument that consists in its entirety of: "Yeah, but ..." [folds arms, scowls, shakes head].

Grant Hutchison

Ken G
2005-Oct-18, 08:07 PM
I see what you mean, and in a way I think we are partly responsible, because when we draw a spinning sphere, we always poke a nice arrow right out of the pole. The axis of the top also leads to this bias, of thinking that a rotation axis is a physical thing, like an antenna poking out. Imagine how much easier it would be to just talk about a free-floating sphere (like a planet) that is rotating, and indicate the rotation by an arrow wrapping around the equator (not an angular momentum vector or a physical axis). Then put another arrow wrapping around at a right angle to it, asking, what will happen if we try to spin it this way and it is already spinning that way? I'll bet you that a lot of people would say, OK, it will spin around like an arrow wrapping around *in between* the two wrapping arrows you've already drawn. Bingo-- that's the correct answer! And you never even had to mention the concept of an axis. I feel that the whole axis concept, although central to the construction of a spinning top (but not a planet), and very useful for angular-momentum-vector thinking, is a complete red herring when it comes to understanding precession for nonmath types. I'd say, use the fact that you really care about a free sphere anyway, as an opportunity to get away from the axis and top concepts altogether. You can always bring the top in later, if they want to see the principle in action. Just a suggestion, as I said your approach sounds very clear to me as well.

grant hutchison
2005-Oct-18, 10:31 PM
The axis of the top also leads to this bias, of thinking that a rotation axis is a physical thing, like an antenna poking out.Ah, familiar territory.
Picture, if you will, a little magnolia-painted room containing a table, six frowning 17-year-olds in Royal Air Force blues, and your increasingly harassed narrator. Each of the 17-year-olds needs to understand something about gyroscopes in order to pass a pre-flight-training exam. Each of them holds one hand loosely curled with the thumb sticking up vertically (fingers, rotation; thumb, axis).
"OK," I say. "Now I try to rotate your gyroscope, John. This way. What does that rotation look like?"
[John flops his hand over on the table obligingly.]
"No, what's the rotation axis? No, of the rotation I'm applying. Show me. No, not with your other hand. Um... OK, yes, that's a problem. Let's use Mike's hand. Mike, you're the applied rotation and John is the gyroscope's rotation. What do you mean you can't bend your arm that way?" [Thinks: I am never going to do it this way again ...]

Grant Hutchison

grant hutchison
2005-Oct-18, 10:34 PM
Then put another arrow wrapping around at a right angle to it, asking, what will happen if we try to spin it this way and it is already spinning that way? I'll bet you that a lot of people would say, OK, it will spin around like an arrow wrapping around *in between* the two wrapping arrows you've already drawn.That's nice. Depends on what illustrations I can use, but these are simple things to diagram clearly.
Thanks!

Grant Hutchison