Undergrad How to quantify gyroscopic precession torque?

[A.T.]

...an internal roll torque reaction to yaw "cancels" an external roll torque...

"Internal torque canceling an external torque" is exactly the kind of confused talk that leads nowhere.

This doesn't change the fact that there is only one external torque that results in precession.

External torques and forces are all we care about.

The gyro initially "drops a bit", and only after the drop has started does the gyro begin accelerating in the direction of precession.

Because of angular momentum and energy conservation the gyro cannot just start precessing, while maintaining exactly the same spin rate and spin axis inclination. The precession motion itself has its own small angular momentum component around the vertical axis, which must be reflected by an equal but opposite change in the vertical angular momentum from the spin.

And it is that small angular momentum component around the vertical axis that you need to remove to stop the yaw-precession.

 

[A.T.]

The torque from the straw is smaller than the torque from gravity, yet the gyro "drops" at a faster rate than it precesses due to gravity alone.

Here a linear momentum analogy that might help to understand why it drops so fast:

Linear momentum:
The force of gravity acting on a body in circular orbit continuously changes direction as the body moves along the orbit, so the linear momentum transferred by gravity doesn't accumulate, it just goes into continuously changing the direction of the bodies linear momentum. When you prevent it from moving tangentially the force of gravity has a fixed direction, so the linear momentum transferred by gravity quickly accumulates, and the body drops to the center fast.

Angular momentum:
The torque from gravity acting on a horizontally precessing gyro continuously changes direction as the gyro precesses, so the angular momentum transferred by gravity doesn't accumulate, it just goes into continuously changing the direction of the gyros angular momentum. When you prevent it from precessing horizontally the torque from gravity has a fixed direction, so the angular momentum transferred by gravity quickly accumulates, and the spin axis drops down fast.

 

[rcgldr]

angular momentum ... gravity

Doing the math from the Wikipedia article, if there was no gravity, and instead the axis support allowed yaw rotation, but not roll rotation, then if a yaw torque was applied to the gyro until the same rate of yaw as gravity induced precession, then the induced roll torque exerted onto the support would have the same magnitude but opposite direction from the torque that gravity would exert if present. Once that same rate of yaw was reached, the yaw torque would go to zero, and there would be a Newton third law like pair of roll torques: the gyro exerting an "upwards' roll torque onto the support that is preventing roll rotation, coexistent with that support exerting a "downwards" roll torque onto the gyro.

The support would need a reactive external torque to prevent the roll rotation, such as being attached to some massive object. Once the yaw torque was removed, then the gyro's change in angular momentum would be balanced by an opposing change in angular momentum of the massive object, and the angular momentum of gyro and object would be conserved. In this closed system, there are no external torques, since the total angular momentum is not changing. This what I meant by the "internal torque" that opposes gravity in the original case.

 

[A.T.]

"downwards" roll torque onto the gyro.

Calling the roll torque "downwards" is a bad idea, even if you put it in quotes. That torque vector is horizontal, and continuously changes direction in the horizontal plane during yaw-precression. This continuous change of torque direction is key to why angular momentum doesn't accumulate during yaw-precression, but does accumulate when yaw-precression is prevented (see post #32). Calling that torque "downwards" doesn't allow to distinguish these two cases, which makes it a particularly bad naming choice here.

... This what I meant by the "internal torque" that opposes gravity in the original case.

Whatever complicated rationale, based on comparing different scenarios, you had for this terminology, it just sounds dead wrong, to say that an internal torque balances an external one for a specific scenario. Just like with your "downward torque" above, your terminology choices make it really hard to follow you.

 

[rcgldr]

Calling the roll torque "downwards" is a bad idea

OK, but the key point was the torques involved with a gyro precessing at some specific rate about a vertical axis is the same for the gravity case or the support that only allows rotation about a vertical axis case, and in the support case, the yaw rate which is the same as the precession rate in the gravity case coexists with a roll torque that opposes the roll torque from the support, and the roll torque from the support is the same as the roll torque from gravity in the gravity case.

 

[rcgldr]

This ambiguity of natural language makes those informal descriptions rather useless, when your goal is to quantify something.

The formula for torque equals rate of change in angular momentum still applies, but when precession is prevented, the rate of change in angular momentum due to a torque perpendicular to what would otherwise be precession acts as if the gyro is not spinning and is just a function of angular inertia. As mentioned in that MIT video, "the gyro just falls". The torque for whatever is preventing precession would account for most if not all the change in angular momentum. The torque that the gyro exerts on whatever prevents precession coexists with a Newton third law torque that whatever prevents precession exerts onto the frame of the gyro.

Right hand rule has to compensate for the fact that there is a torque that exactly opposes precession.

 

[A.T.]

This ambiguity of natural language makes those informal descriptions rather useless, ...

"the gyro just falls".

This is exactly the ambiguous language that is not very useful or even misleading. What does "the gyro just falls" mean exactly here?

The term "just falls" implies (or at least strongly suggests) that as soon it touches the precession-obstacle, the gyro axis moves in exactly the same way, as it would if the gyro was not spinning at all, and was just released, so it "just falls". Is this really true? Was the exact motion of the gyro axis at the precession-obstacle measured, and compared to a non-spinning gyro that was just released?

The term "falls" is a bad choice, even for the non-spinning gyro case, because it's not free falling.

 

[rcgldr]

From Caltech Feyman Lecture Hall - "You'll also notice that if I stop its precession, it simply falls"". A slightly out of balance gyro in this example so the rate of fall is slow.

youtube - Caltech - stop precession

In this 1974 Laithwaite lecture, he gets some stuff wrong, but in this video clip you can see that when precession stops, the gyro just falls:

youtube - 1974 Laithewaite gyro

The part about precession having no angular momentum doesn't take into account that the force on the peg still has to generate the torque the correlates with the rate of change in angular momentum as the gyro falls.

On a motorcycle ridden in a straight line, friction prevents precession, and the bike will tip over as if neither wheel was spinning (the bike simply falls over). Not mentioned is that the lateral forces on the tires would have to generate the torque related to the rate of change in angular momentum of the front and rear wheels.

Wiki - precession prevented

Steering the front wheel outwards (counter-steering) does create an inwards roll torque, but it is a small compared to the inwards torque related to the tires out-tracking from under the motorcycle.

Wiki - roll torque from steering front wheel

 

[A.T.]

you can see that when precession stops, the gyro just falls:

No. I cannot see that the gyro "just falls", because the exact definition of "just falls" is not provided.

If we adopt the definition in post #37, then you cannot properly determine that from fractions of a second in a video of a demo, where nothing is properly measured, as already explained:

Was the exact motion of the gyro axis at the precession-obstacle measured, and compared to a non-spinning gyro that was just released?

In the Caltech video it's rather obvious that it doesn't "just fall" according to the definition in post #37. If you don't like that definition of "just falls", then provide your own. But posting examples of other people using this or similar undefined terms is just as pointless, as your use of them. And I don't quite understand what the point in reviving this old thread is, if you have nothing new to add.

 

[rcgldr]

I don't quite understand what the point in reviving this old thread is, if you have nothing new to add.

New to this thread: The law of torque versus rate of change of angular momentum still applies: the torque required to prevent precession is equal to the rate of change of angular momentum. Restated, the torque that prevents precession along one axis causes a gyro to instead to precess in the direction of and at the rate of change in angular momentum. In the case where gravity exerts a torque onto the gyro, the torque that prevents gravity related precession causes the gyro to accelerate downwards so that there is zero net torque related to gravity, and the gyro appears to "just fall". Right hand rule also applies in this situation, there has to be zero net toque due to gravity otherwise the gyro would have a component of precession that was not vertical.

Another example is at the start of this clip:

MIT large gimbal mounted gyro

How much torque was needed to hold the yellow frame in place while the gyro was being rotated from a vertical orientation to a horizontal orientation. Note that the person grips the yellow frame with his entire left hand, while rotating the gyro from vertical to horizontal with just his right thumb and finger. The rest of that clip shows normal precession.

 

[A.T.]

New to this thread: The law of torque versus rate of change of angular momentum still applies:

What is new about that? It was stated in this thread several times already.

How much torque was needed to hold the yellow frame in place while the gyro was being rotated from a vertical orientation to a horizontal orientation.

To compute a force acting on a body, you need to know all the other forces acting on it, and the rate of change of its linear momentum.

To compute a torque acting on a body, you need to know all the other torques acting on it, and the rate of change of its angular momentum.

 

[rcgldr]

What is new about that? It was stated in this thread several times already.

The new part is that the torque opposing precession coexists with zero net torque in the direction of change of angular momentum (the direction of the original torque). The zero net torque in the direction of change of angular momentum is what I was missing before. In the case of gravity induced torque, the torque that prevents precession changes the precession to one that accelerates the gyro downwards so that there is zero net torque from gravity, which is why the gyro "just falls".