Torque and Work

## Question:

Why and how is torque different from work? What is a system in equilibrium with torque? What are some examples of equilibrium of torque in our everyday world?

Torque and work are expressed in the same units but they are different physical quantities, torque being a vector and work being a scalar.

First to deal with work a bit. Imagine a box of rocks sitting on a table. If we push on that box so that it slides along the table top in the direction we are pushing, we will be doing work. The definition of work is the product of the magnitude of the net force applied times the distance traveled. Both the magnitude of a force and distance are scalar quantities so work, being the product of the two, is a scalar. Scalars are expressible as a single number. The units on work in SI units would be the Newton meter.

Now for torque. Imagine a heavy pulley with a rope running over it. By pulling on the rope we can cause the pulley to begin turning on its axis. The torque is defined as a vector found by taking the vector cross product of the force vector and the vector from the axis of the pulley to the point of contact between the pulley and the rope. Being the cross product of two vectors, torque is itself a vector perpendicular to both the direction of the force vector and the direction of the radius vector. Vector quantities require more than on number to specify them. The units on torque are also Newton meters but different from work because of the vector nature of torque.

When a system is in equilibrium with regard to torque, its rotary motion is constant over time. If it was not rotating when we found it, it will never rotate as long as it remains in equilibrium with regard to torque. If it was rotating when we found it will continue to rotate with the same angular velocity as long as it remains in equilibrium with regard to torque. An object requires an unbalanced torque to either speed up its rotation or slow it down.

When an automobile is stopped, its wheels are in equilibrium with regard to torque. When I step on the gas and release the brake, I upset that equilibrium causing the wheels to roll and the automobile to move. The automobile will accelerate until the torque applied through the axle is balanced by the torque applied through contact with the road. At that point the wheels are back in equilibrium again so they rotate at constant speed until I do something else to upset the equilibrium, either speeding up by increasing torque applied through the axle or slowing down by decreasing axle torque or increasing the drag of the vehicle through the brakes.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ