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RoyalCat
#3
Feb21-10, 04:20 PM
P: 671
You've got your directions wrong. Torque is a vector quantity. That means that when you add two or more torques together to find the net torque, you must do so with due regard to sign.

The simplest way to add torques correctly, would be to use your intuition to find the "sense" of rotation of every force vector. For instance, in your example above, the left force tries to spin the rod counter-clockwise, while the right force tries to spin it counter-clockwise as well. Therefore, the net torque is the sum of the two, since the two torques have the same sense of rotation.
Were they opposite, then the direction of rotation would be determined by which is the greater torque.


A more complete approach that you'll need for further studies, when keeping track of signs is a bit more important:
How do we take care of that sign, then? We define torque as a vector perpendicular to the plane of rotation (The plane of the lever arm vector and the force vector).

And we determine the sign by way of the right-hand rule (Wiki link:http://en.wikipedia.org/wiki/Right_hand_rule)

Torque as a vector is defined as:
[tex]\vec \tau = \vec r \times \vec F[/tex]

Applying it to the situation above, taking the torque about the axis through the center of the rod, taking the positive direction as the one coming out of the plane of the page (If this is Greek to you, read up on the article on the right hand rule and vector cross product), we see a positive torque whose magnitude is [tex]2Fr[/tex].