Torque (changing reference frames and adding)

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Discussion Overview

The discussion revolves around the transformation of torque vectors between different coordinate systems and the procedure for adding torque vectors that act about different axes. It encompasses theoretical aspects of torque in physics and the implications of coordinate transformations.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • João questions whether a homogeneous transformation matrix, which includes both rotation and displacement, can be used to change the coordinate system of torque vectors.
  • One participant suggests using only the rotation part of the transformation matrix for the torque vector, indicating that displacement is necessary for transforming the point of application of the torque.
  • João inquires about the net torque resulting from the addition of two torque vectors.
  • Another participant explains that to compute the net torque around a third point, one must know the force sums associated with the torques, and that in cases where the forces sum to zero, the torques can be added directly.
  • A caution is raised regarding the transformation of torque vectors between right-hand and left-hand coordinate systems, noting that a negation of the torque vector is necessary when applying the transformation matrix.

Areas of Agreement / Disagreement

Participants express differing views on the procedure for adding torque vectors and the implications of coordinate transformations. There is no consensus on the exact procedure for determining the net torque when the torques are about different axes.

Contextual Notes

Limitations include the need for additional information about the forces associated with the torques to compute a net torque around a third point, as well as the dependence on the definitions of coordinate systems when transforming torque vectors.

joaozinho
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Hello there

I have 2 questions:
1. Can one change the coordinate system of torque vectors through a homogeneous transformation matrix with both rotation and displacement?

2. What's the procedure to add two torque vectors about different axes?

Thanks in advance,
João
 
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joaozinho said:
1. Can one change the coordinate system of torque vectors through a homogeneous transformation matrix with both rotation and displacement?
Use just the rotation part to transform the torque vector. The full transformation with displacement must be applied to transform the point around which the torque acts.

joaozinho said:
2. What's the procedure to add two torque vectors about different axes?
The get the net torque acting on an object you just add them, regardless around which axis they act.
 
Thank you! That was a quick reply!
So if I add the two torque vectors, the result will be the net torque about what point?
 
joaozinho said:
So if I add the two torque vectors, the result will be the net torque about what point?
In general, if just know two torques acting around two different points, you cannot compute a net torque around some third point. You also have to know the force sums of the forces for each of those two torques. Then the total net torque around some third point is the sum of the two torques, plus the two torques from those force sums acting at the two different points.

In the special case, when each of the two torques is generated by a force set which sums to zero, you simply add the two torques. The point of application of that net torque is arbitrary.

Also a word of caution on your first question regarding transforming a torque vector to a different coordinate system via a matrix: If one is a right-hand-system and one a left-hand-system you have to apply the 3x3-matrix and negate the torque vector.
 

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