VtSkier wrote:

In 2) above, I'm still troubled by the wrench
on the nut example. There is no component torque
here, yes? Yet there is no movement of the nut
until the force applied to the lever arm overcomes
friction to allow the nut to move.

Yes, there is component torque here. Let's use another example without
vectors. Vectors are sooo last century anyway and just a figment of
our imagination. Quaternions are where it's at. But anyway, Let's say
we have a spindle between us. I put a torque wrench on the spindle on
one side, you put a torque wrench on the other side. I apply a torque
of 5 Nm on my wrench. Now we have one component of the total torque,
equal to what the torque wrench reads. 5 Nm. Notice we haven't
discussed motion yet, because it doesn't matter. Now you apply a
torque on your wrench in the opposite direction, equal to 5 Nm. So we
have two component torques which exist. Mine, 5 Nm and yours, -5
Nm. Two components of the sum. These are two *real* torques. +/-5
Nm. And there is no motion, but the torques exist. My arm gets tired
because I am applying a torque, and your arm hurts becasue you are
applying a torque. They just happen to balance and there is no motion
because the total torque is zero. Zero motion and two torques. Torques
*do* exists even in the absence of work or motion.


-klaus