Torque (changing reference frames and adding)

[joaozinho]

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

 

[A.T.]

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.

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.

 

[joaozinho]

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?

 

[A.T.]

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.