Why when the axis is pivoted, there is no torque in its direction?

[LCSphysicist]

Homework Statement

Why when the axis is pivoted, there is no torque in its direction?

Relevant Equations

All below.

I want to say [the bodies is under gravity field]:

There cannot be torque alonge AB "since it is pivoted"

There cannot be torque alonge AB "since it is pivoted"

i think i am missing something.

 

[Halc]

I think it says that there cannot be a torque vector along the direction of the axis, at least not applied by the bearings where the axis is held (A and B in the upper picture).

I find it bad form that angular velocity ω is depicted as physical curved arrows in the upper picture and as a vector (labeled 'Spin') in the lower picture. The ω vector is pointing kind of to the front right and the Ω vector would be pointed up in the first picture.
The lower picture doesn't show anything being done to the axis A-B, but it looks like they want to apply torque or rotation to the base in the upper picture. It isn't fully described. There will then very much be torque applied 'to' A and B, but not torque 'along' A and B. The torque vector applied to A and B would (for a while) point upward instead of along the axis. As far as I can tell, that's what is meant. The text quoted doesn't seem like the original text. The precession of the wheel will nevertheless generate rotation 'along' the A-B axis. The wheel is not free to move in all directions, so angular momentum will be lost to the base/ground.

 

[wrobel]

Homework Statement:: Why when the axis is pivoted, there is no torque in its direction?
Relevant Equations:: All below.

There cannot be torque alonge AB "since it is pivoted"

I think it means that "since it is pivoted and there is no friction in the hinges A and B"

 

[Lnewqban]

Homework Statement:: Why when the axis is pivoted, there is no torque in its direction?
Relevant Equations:: All below.

The whole idea of the contraption is that regardless the movement of the base, the rotating mass remains on its rotational plane and can be used as a spatial reference (gyroscope principle).
Why having articulations (pivot points) of reduced friction between both is important?

 

[LCSphysicist]

Yes, it is pivoted without frictionless.
I think this is important cause the motion will not be dumped, i think the friction would somehow apply a torque.
Without this force, we will have just the normal in a vertical plane, whose torque is not in AB direction.
Even so, i am in a little doubt. In all the cases there is no torque in the direction of the axis pivoted, or just in this special cases?

 

[LCSphysicist]

This question too, since it is pivoted, we could apply conversation of angular momentum about it. Because there is no torque about it.

 

[Lnewqban]

... Even so, i am in a little doubt. In all the cases there is no torque in the direction of the axis pivoted, or just in this special cases?

What they mean is that torque can't be transferred through a pivot in the direction of its axis.

Let's say the base is connected to the structure of an airplane that is banking to turn.
The body of the airplane is doing some mechanical work on that base by transferring or applying a rolling torque in the same direction of the axis of the pivots.

The same torque would be transferred to the rotating mass of the gyroscope, forcing it to deviate from its original vertical plane of rotation, which we need to create an artificial Earth's horizon that serves us as spatial reference during poor visual conditions.

If those two pivots exist, then that disturbing torque can't be transferred to the wheel, which will happily remain spinning on the needed vertical plane of reference.
The pivots receive that disturbing torque but, because their frictionless nature, are unable to create a reactive torque of equal magnitude and opposite direction (Newton's law #3).

The pivots can still transfer linear forces and disturbing movements from the base to the spinning wheel, and even any torque that is applied in a direction that differs from the direction of the pivoted axis.

That is the reason for mechanical gyroscopes to have two pivoted axes arranged at 90 degrees between them, in such a way that they work as a Cardan type coupling, isolating the spinning wheel from any torques, regardless the direction those may come from.

 

[Lnewqban]

View attachment 263479
This question too, since it is pivoted, we could apply conversation of angular momentum about it. Because there is no torque about it.

Although I don't understand this problem, whatever torque that bug is generating while walking around the ring can't be transferred to the table via the pivots; therefore, the ring is free to tilt around the pivots.

 

[haruspex]

Yes, it is pivoted without frictionless.
I think this is important cause the motion will not be dumped, i think the friction would somehow apply a torque.
Without this force, we will have just the normal in a vertical plane, whose torque is not in AB direction.
Even so, i am in a little doubt. In all the cases there is no torque in the direction of the axis pivoted, or just in this special cases?

Perhaps your confusion is that as the platform is rotated the cradle holding the disc will rotate about the AB axis. But that does not imply a torque of any significance; the cradle+disc is merely moving so as to maintain its angular momentum. To inhibit that rotation, e.g. by friction, would require a torque.