Torque, point or axis of rotation

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Discussion Overview

The discussion revolves around the concept of torque, specifically whether it is calculated with respect to a point or an axis of rotation. Participants explore the implications of these definitions in both two-dimensional and three-dimensional contexts, as well as the relationship between torque and angular momentum in gyroscopic motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether torque is calculated with respect to a point or an axis, noting conflicting information from various resources.
  • Another participant asserts that in 2D, torque is about a point, while in 3D, it is about an axis, and emphasizes that angular momentum and torque are not regular vectors.
  • A participant raises a concern regarding the application of the formula T = r × F in 3D, questioning how torque is determined when r is defined with respect to a point that has infinite axes of rotation.
  • Another reply suggests that the axis of rotation is indeed the vector perpendicular to both r and F, which aligns with the direction of the torque vector as defined by the cross product.
  • A participant seeks clarification on the term "pseudovector" in the context of torque.

Areas of Agreement / Disagreement

Participants express differing views on the definition of torque in relation to points and axes, and the discussion remains unresolved regarding the implications of these definitions in practical applications.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the definitions of torque and angular momentum, as well as the mathematical steps involved in applying the torque formula in three-dimensional space.

bgq
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Hi,

1) Do we calculate torque with respect to a point or with respect to an axis?

I have read them both in different resources, and so I am confused!

2) If we calculate torque with respect to an axis, many introductory textbooks discuss the motion of the gyroscope by considering how the torque affects the angular momentum, but there is a problem that the angular momentum is specified with respect to a different axis of rotation than that of the torque (The angular momentum is about the axis of the wheel, while the torque is about the axis passing through the pivot and perpendicular to the first one); how can we resolve this?

Thanks to any helps.
 
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In 2D, a torque is about a point.
In 3D it is about an axis.

Just the same way that a rotation is about a point in 2D and an axis in 3D.
But note: angular momentum and torque are not like regular vectors.
per your example, the same texts should show you the math of how the torque affects the angular momentum.
 
Simon Bridge said:
In 2D, a torque is about a point.
In 3D it is about an axis.

Thanks to your reply.

My problem is that when applying the formula T = r × F in 3D, r is determined with respect to a point where there are infinite axis of rotations passing through this point, so T is determined with respect to which axis?
 
My problem is that when applying the formula T = r × F in 3D, r is determined with respect to a point where there are infinite axis of rotations passing through this point, so T is determined with respect to which axis?
... the axis of rotation of course... which is a vector perpendicular to both r and F... points in the same direction as the pseudovector T. That is what the direction part of the cross product is for.
 
Simon Bridge said:
... the axis of rotation of course... which is a vector perpendicular to both r and F... points in the same direction as the pseudovector T. That is what the direction part of the cross product is for.

What is meant by pseudovector?
 
Thank you very much.
 

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