Torque question -- why defined as r×f and not f×r?

  • Context: Undergrad 
  • Thread starter Thread starter Vijay.V.Nenmeli
  • Start date Start date
  • Tags Tags
    Torque
Click For Summary

Discussion Overview

The discussion revolves around the definition of torque as the cross product of the position vector (r) and the force vector (f), specifically addressing why it is defined as r×f rather than f×r. Participants also explore the implications of using perpendicular vectors in torque calculations and the validity of this approach.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that the definition of torque as r×f is a convention, similar to other directional conventions in physics.
  • It is noted that the order of the cross product is significant because r x f does not equal f x r.
  • One participant questions whether the use of perpendicular vectors is merely a simplification and how it affects calculations, proposing the idea of using a vector at a 45-degree angle instead.
  • Another participant argues that while a 45-degree vector is not "wrong," the use of perpendicular vectors is more convenient and leads to better results in calculations.
  • There is a discussion about the limited number of vectors that can be perpendicular to the plane formed by f and r, emphasizing the two possible directions (up and down) for the torque vector.

Areas of Agreement / Disagreement

Participants express differing views on the nature of conventions in physics, particularly regarding the definition of torque and the use of perpendicular vectors. There is no consensus on whether the perpendicular approach is inherently superior to other potential representations of torque.

Contextual Notes

Participants acknowledge that the choice of vector representation can influence calculations and outcomes, but they do not resolve the implications of using different angles for torque representation.

Vijay.V.Nenmeli
Messages
3
Reaction score
0
Hello everyone,
Quick question.
Could anyone explain to me why torque is defined as r×f and not f×r.Also, how do we know that taking the direction of the vector as perpendicular to the plane is valid?
Thanks in advance
 
Physics news on Phys.org
Vijay.V.Nenmeli said:
Hello everyone,
Quick question.
Could anyone explain to me why torque is defined as r×f and not f×r.
It's a convention, just like choosing the negative direction of the x-axis to be to the left of the origin is a convention. You could do it the other way as long as you were consistent about doing it the other way everywhere - for example, you would also have to switch the order in the definition of angular momentum.

Also, how do we know that taking the direction of the vector as perpendicular to the plane is valid?
It leads to a mathematically convenient way of describing torques and angular momenta. As these have both magnitude and orientation in space, it's natural to describe them as vectors perpendicular to the plane of movement. As a historical note, torque and angular momentum were discovered before vector calculus was invented... There's a thread on this history somewhere around here.
 
The order here is important because the cross product does not commute; that is r x F ≠ F x r .
 
Thanks a lot Nugatory,
But this method of taking perpendicular vectors is, as I see it, merely a way to simplify calculations. Does it affect the calculations in any way I.e If I were to take a different vector to represent torque, say one that was aligned at 45 degrees to the plane of F and R,, I'd get a different vector. Less convinient to work with, maybe, but how do we know that the 45 degree vector is not right and the perpendicular is
??
 
Vijay.V.Nenmeli said:
but how do we know that the 45 degree vector is not right and the perpendicular is?
A convention is neither right nor wrong.
 
Vijay.V.Nenmeli said:
Does it affect the calculations in any way I.e If I were to take a different vector to represent torque, say one that was aligned at 45 degrees to the plane of F and R,, I'd get a different vector. Less convenient to work with, maybe, but how do we know that the 45 degree vector is not right and the perpendicular is??

There are exactly two vectors (of a given magnitude) that can be perpendicular to the plane of F and R: one up and one down. There are an infinite number of vectors of that magnitude that can be at a 45 degree angle to that plane (imagine a cone with its point just touching and its axis perpendicular to the plane - all vectors along the surface of that cone are at the same angle relative to the plane). Because there are only two possible rotations in a plane, clockwise and counter-clockwise, it's easy to map the the two possible directions of a perpendicular vector to the two possible rotations.

That doesn't make a 45-degree convention "wrong" (as A.T. has pointed out above, a convention cannot be wrong), but it is a fairly strong hint that we'll get better answers faster if we use the cross-product.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 37 ·
2
Replies
37
Views
5K