Why can't the units of work and torque be interchanged? When I'm studying about work and torque, I found that their unit are the same. But, why don't we use Joule (unit of work) instead of Newton-meter (unit of torque)? Since $\mathrm{1\ Joule = 1\ Nm}$, why can't they be interchanged?
 A: They have the same SI deriviation, but very different connotations. Not everything in science that is formally equivalent is semantically equivalent. There is a connection between torque and work, as you are applying a force somewhere and moving a distance. However, torque is only an indirect measure of force. For example, why does the required torque double when you halve the lever arm? Its not because the opposing weight got twice as heavy (i.e. exerting more force) but that you will be applying a force through only half the distance while the opposing weight still moves the same distance. Therefore, the same work must be packed into a smaller space, requring the force to go up. This concept is nicely packaged in the torque, which allows you to multiply the torqe (Nm) by a dimensionless unit(radians), to get the work done (joules). Since angular movement is dimensionless, the dynamic component of the work equation must have the same units of energy, but it is a very different concept.
Anayway, that was a perhaps long-winded answer. I've thought a similar thing myself. Lots of "named" units have the same SI deriviation: e.g., Energy, Torque, and Pressure all have the same SI units. They are very closely related to each other, but it would not makse sense to say I need a 100 pascal battery, although a pressure vessel at 100 pascal would contain some measure of energy.
A: Torque and work can not be interchanged because they do not represent the same thing. 1 Joule is the amount of energy required to move an object against a force of 1 N by 1 m.
1 Nm of torque, on the other hand, is the torque obtained if you apply a force of 1 N att a force arm of 1 m.
Two totally different concepts, not equivalent at all.
