[Jaaanosik (OP)]

[momentum] is a vector ... composed of direction and magnitude, but not location.

That's an interesting comment.
The vector of the same direction and magnitude but not the location.
If the vector is not in the same location within the reference frame then the acceleration effect will be different based on the location. Correct?
What I mean is that the outside frame sees the geometric center shifted.
If the angular momentum vector is shifted to the geometric center then what happens when the axle, now off center, gets accelerated?

If you read my comment, I said the momentum doesn't have a location, so the nonexistent location cannot be shifted anywhere. Any yet I see at least four references to the location of the momentum above (bolded), which makes no sense.

It not having a location means that I can apply a certain torque anywhere on the object and it will have an identical effect on its angular momentum regardless of where the torque is applied.

Similarly, I can apply linear force anywhere on the object and it will have an identical effect on its linear momentum regardless of where the force is applied. That's what it means for momentum not to have a location.

That's not the case.
A vector cannot be 'hanging' with no location/position to start.
The linear and angular momentum vectors start in the center of mass.
If a rigid body is pushed by a force vector and this force vector is not going through the center of mass then the end result is a change of linear and angular momentum of that rigid body.
If the rigid body is pushed by the force vector through the center of mass then the end result is only a change of the linear momentum.

[Jaaanosik (OP)]

Going back to the relativistic Hall effect paper.






The first diagram analysis, right side (b), is done for the first outside frame (1OF).
The second diagram analysis, right side (b), is done for the second outside frame (2OF) that is moving at 2v in the first outside frame.
The relativistic addition is done between the frames so the velocity is not >c.
The rest frame (a) is in the middle between 1OF and 2OF.
Let us consider the velocity 0.866c.
The rest frame moves to the left at v=0.866c in 1OF.
The rest frame moves to the right at v=0.866c in 2OF.
The text book says the centroids are frame dependent.
The (b) analysis is correct for both frames.
The relativity appears to be symmetrical.
The axle acceleration does not predict the same result!
The acceleration in 1OF decreases the angular momentum, but the acceleration increases the angular momentum in 2OF.
This appears to be a contradiction, meaning only one can be correct.