[EricH]

Darn it, that's what I get for trying to do thermodynamics and dynamics-type unit-crunching after 11PM when I've got a headache. At least I'm not trying my homework in said subjects at this time...

As for torque, the only time it wouldn't share units with power would be if the force generating it was directed directly away from the axis of rotation, along the radius vector. Then torque goes to zero. Or if the force is acting at the axis of rotation, directed away from it (or towards it).

As long as you can get a component of force that is perpendicular to the radius, at a distance greater than zero, you can get the torque. Force *distance, where the distance is specifically defined as the radius between the force and the axis of rotation.

A statics course uses the same type of math to calculate the moment on a point in a beam.