Angular velocity, Angular Momentum and Torque considered vectors to explain gyroscope precession and related phenomena?

Question

Are angular velocity, angular momentum and torque "real" vectors in the sense that acceleration and force are? Or are they only considered vectors to explain phenomena like gyroscope procession? Or are they considered vector quantities for other reasons?

It seems to be the case that we only assigned a vector to these rotational quantities because it's a convenient way to keep track of them. A disk rotating in the x-y plane would have an angular velocity vector along the z-axis. The faster the rotation, the "longer" the vector. If the rotation reverses direction, the arrow flips upside down.

But with things like gyroscope precession, the waters are muddied. Are these quantities really vectors? Or just bookkeeping constructs?

@kevin012 Okay. Let us do a simple thought experiment: Let us suppose ( if possible) that they are not vectors(if this makes any sense) then do we get the precession? — Hiro, Jul 18 '20 at 15:15
I believe you are asking this: "are angular velocity, angular momentum and torque real vectors like acceleration? Or are they only considered vectors to explain phenomena like gyroscope procession. Or are they considered vectors for other reasons?" Am I correct in assuming that this is what you want to know? — novawarrior77, Jul 18 '20 at 20:25
Alright, I have submitted an edit on your behalf. I was afraid of the closing of the question, because it is an interesting one and I want to see it answered. — novawarrior77, Jul 19 '20 at 04:09
@novawarrior77 Thanks for the edit, it also clarified my confusion. — Hiro, Jul 19 '20 at 09:47

Cleonis · Answer 1 · 2020-07-21T15:57:54.267

Torque, angular velocity and angular momentum are not inherently vectorial quantities.

One way to demonstrate that is to consider motion in some space with more spatial dimensions than our familian three spatial dimensions.

In a space with 4 spatial dimensions the following applies: to specify orientation of a state of rotation you need to specify the plane of that rotation. And obviously this extends to all higher dimensions.

In a space with 3 spatial dimensions it is equally the case that in order to specify the orientation of the rotation you need to specify the plane of rotation. It's just that with a space with 3 spatial dimensions every plane has a single vector that is perpendicular to that plane. Representation of angular quantities in vector form takes advantage of that opportunity.

This is why the vector representation of angular quantities needs a parity convention, in this case that convention is the right hand rule

In mechanics using vector representation for torque, angular velocity, angular momentum offers only limited explanatory power. The vector representation should be used as a bookkeeping device.

An angular momentum vector is an abstraction, it is an indirect representation. (Angular momentum is the linear momenta of all constituent parts of an extended object, integrated around the axis of rotation.)

For an explanation of gyroscopic precession see my 2012 answer to the question: What determines the direction of precession of a gyroscope? In that explanation the concept of angular momentum vector is not used.

score 0 · Answer 2 · answered Jul 19 '20 at 15:19

The vectors describing rotation are chosen along the axis of rotation because that is the only fixed direction in a rotating system. Given that choice, they do a good job of representing the magnitude and direction of rotational quantities, and as long as the axle remains fixed, they relate to each other and the various linear quantities in a straightforward and predictable fashion. With an axle that changes direction, I'm assuming that experiments were performed to verify that the vector formulas being used in two or three dimensions were giving accurate results.

Angular velocity, Angular Momentum and Torque considered vectors to explain gyroscope precession and related phenomena?

2 Answers2