Gyrocompass motion: Zero torque in the free axis

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Discussion Overview

The discussion revolves around the concept of torque in the context of a gyrocompass, specifically addressing why there is zero torque along the free axis (y-axis) when the system is allowed to swing freely. Participants explore the definitions and implications of torque in rigid body motion.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that the pivots at A and B allow the gyrocompass to swing freely about the y-axis, suggesting that this results in no torque along that axis.
  • Another participant emphasizes the definition of torque, stating that if an applied force passes through an axis, it produces no torque around that axis.
  • A participant asserts that if the forks A and B are frictionless, they cannot apply any force to the cylindrical axle that does not pass through its axis, supporting the claim of zero torque.
  • There is a discussion about the cross product R x F being zero, with one participant stating it is zero because the angle between R and F is zero, while another later suggests it could also be zero if R is zero or if the angle is 180°.

Areas of Agreement / Disagreement

Participants generally agree on the definition of torque and its implications for the gyrocompass system, but there is some disagreement regarding the specific conditions under which the cross product R x F equals zero.

Contextual Notes

There are unresolved aspects regarding the definitions of R and F, as well as the conditions under which torque is considered zero, which may depend on specific interpretations of the system's mechanics.

RicardoMP
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Hi!
At the moment I'm studying rigid body motion, more specifically, the gyrocompass. As you can see in the attached picture (Introduction to Mechanics -Kleppner-Kolenkow-Chap.7), the gyrocompass rotates about the z axis and the spin angular momentum is reoriented towards the z axis, creating a angular momentum along the AB axis. As I've read, the pivots at A and B allow the system to swing freely about the y-axis (which is along AB), so there can be no torque along the y axis. Why is that? Why is the torque along any free axis zero? I know that there are a couple of contributions to torque along the y axis, for example, the change of direction of the spin angular momentum. Why must the sum of all these contributions be zero? My objective is to understand intuitively this concept so any time I'm faced with such an axis, I immediately assume that the torque along it is zero.
Sorry for the long post and thank you in advance!
 

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RicardoMP said:
As I've read, the pivots at A and B allow the system to swing freely about the y-axis (which is along AB), so there can be no torque along the y axis. Why is that?
Look at the definition of torque, if an applied force passes through an axis, then it produces no torque around that axis. If the forks A & B are frictionless, can they apply any force to the cylindrical axle, that doesn't pass right through it's axis?
 
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A.T. said:
Look at the definition of torque, if an applied force passes through an axis, then it produces no torque around that axis. If the forks A & B are frictionless, can they apply any force to the cylindrical axle, that doesn't pass right through it's axis?
Oh! Indeed! It is that simple. And so, the sum of all contributions to the torque along that axis equals the cross product R x F, in this case is zero, since the angle between R and F is zero.
Thank you!.
 
RicardoMP said:
the cross product R x F, in this case is zero, since the angle between R and F is zero.
R x F is zero because R is zero, in this case.
 
Ah yes, of course! My bad!
Thank you! :)
 
RicardoMP said:
Ah yes, of course! My bad!
Thank you! :)
Well depending on what R is meant to be, you can also say: R x F is zero because the angle between R and F is 180° .
 

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