The Gyroscopic Effect: Precession, Nutation, & Boomerang Return

[Trying2Learn]

TL;DR Summary

Spin, Precession and Nutation (the gyroscopic effect)

Hello!

I am not sure I will ask this correctly, but please allow me to try.

I understand that if a disk is spinning, and we precess it, we will "feel" a force that will nutate the disk (e.g.: the fidget spinner)

This is the gyroscopic effect.

I understand, mathematically, the origin of spin, precession and nutation (and, yes, I am aware that the Tait-Bryant angles reveal this as pitch, yaw and roll; but let me ignore that second category of rotations).

So, I can set up a rule (a blind rule that circumvents the math, but a rule nonetheless): a disk spins, we precess it, and we "feel" a force that induces a nutation. The order of this follows the right hand rule with the outcome being the nutation (using the paraphernalia of the cross product: spin crossed into precession is nutation).

Now, is the nutation a kinematic motion or a kinetic forced response?

Both precession and nutation involve a rotation but how do we view this in our minds?

For two examples:

1. If I throw a boomerang, the following happens: it spins, the wing like nature of the "airfoil" induces a nutation (kinetic or kinematic?), and the result is a precession (that brings back the boomerang--so, kinematic).
2. I put a spinning disk on a boat and precess it. This induces a nutation, which could prevent ship roll.

In the first case, the disk spins and a airfoil moment acts (which looks like a kinematic rotation, but results from a moment) and that induces a rotation (called precession) which returns the boomerang.

In the second case, the disk spins and we precess the disk (and as this is explained in the literature, it is a rotation -- requiring a moment in and of itself, yes, but still a rotation) that induces a moment.

In other words, I have comfort in the SECOND case, but NOT the first. I can map out the order of spin and precession for the boat.
In the first case (of the boomerang), I can imagine the airfoil such that it induces a rotation, but why is the result not a FORCE that causes the precession.

I do not know if I am making any sense. I cannot grasp whether the math (and the blind rule) should be kinematic or kinetic.

In other words, forget the shape of the boomerang and throw a disk. What is the air doing? Is it nutating it or precessing it?

Oddly, I follow the math, but I cannot formulate what comes first, the chicken (the force) or the egg (the motion).

Or to put this another way, if I spin the boomerang and assume the airfoil moments are such that it induces a PRECESSION, then we get a NUTATINO that returns the boomerang and the cross product works. Except that now I am asserting that the boomerang returns because of a NUTATION not a precession. And that appears to contradict the literture that assert that the boomerang returns due to PRECSSION.

 

[mpresic3]

Summary:: Spin, Precession and Nutation (the gyroscopic effect)

I understand that if a disk is spinning, and we precess it, we will "feel" a force that will nutate the disk (e.g.: the fidget spinner)

To be honest I have no idea what you are asking here or further on in the post. From the very beginning, what do you mean we precess it? Do you mean you have a spinning disk, and you tilt the axis of spin, and you release it? Do you mean you give the spin axis a push or a pull upon release. Do you release the spin axis with a prescribed orientation and angular velocity? All of these variables will determine whether the gyro precesses and nutates. It make no sense to say we "precess" the spinning disk. Likewise, you say we will feel a force that will nutate the disk. Who is we feeling the force? Are you placing yourself on the spinning disk? I read further in your question and I see more unclarity.

Precession does not induce nutation. You can have precession without nutation, in prescribed circumstances, i.e. carefully prescribed initial conditions. The boomerang is not a good example when learning all this for the first time. It would probably be better to understand the ideal case of force free motion rather than aerodynamics.

Summary:: Spin, Precession and Nutation (the gyroscopic effect)

In the second case, the disk spins and we precess the disk (and as this is explained in the literature, it is a rotation -- requiring a moment in and of itself, yes, but still a rotation) that induces a moment.

If you find literature that states "we precess the disk... etc", you should run to a good intermediate mechanics textbook like Marion/ Thornton or Symon, or many others or advanced textbooks, like Goldstein, and away from any source that presents the material at best informally and does not present the material precisely, with with clarity.

Likewise, when asking a question, try to phrase it by specifying the system, and the initial conditions and the phenomena you wish to understand. We precess the disk, is not as good as we carefully release the spin axis, and the spin rates are chosen, so that the disk does not nutate, if this is what you mean?

First, in trying to learn rigid body mechanics, you should probably slow down. Learn the basics first. Be very careful in using definitions of precession, nutation. Carefully consider the simplest examples that exhibit the phenomena, e.g precession, until you understand them thoroughly. Some physics professors consider rigid body mechanics as the most complicated concept in undergraduate physics. You can probably find this quote on these forums. I can supply the quote if necessary.

 

[hutchphd]

You could add some Feynman:
https://www.feynmanlectures.caltech.edu/I_20.html

 

[hmmm27]

@OP what do you mean by " "feel" " ?

Boomerang : in forward flight the advancing airfoil on one side provides more lift than the retreating airfoil on the other. A roll is induced which sets up precession/nutation.

Frisbee : the air does almost nothing to affect orientation. You will of course get side or back slip due to any initial side or back tilt.

My turn : why are boomerangs 'V' shaped ?

 

[ardnog]

My turn : why are boomerangs 'V' shaped ?

Probably tradition, as there are other returning shapes such as a trifoil or cross.

EDIT: It's possible the 2-armed L or V shapes are easier to fabricate with primitive tools. That's not a physics question though. You'd need to ask a carpenter etc.