torque

An interaction which produces rotation.

Motivation for Concept

Forces applied to a body in an attempt to produce rotation will have different effects depending upon both their direction of application and their location of application. Most people have either accidentally or purposely experimented with opening a door by applying a force near the hinges and found it to be an inefficient procedure. Obtaining rotation is much easier when the force is applied far from the hinges (hence the placement of door handles opposite the hinges).

Location alone, however, is not enough to guarantee effective rotation. Consider another experiment. Suppose that you open a door so that it is ajar. Position yourself at the edge of the door opposite the hinges and push directly along the door toward the hinges. The door will not rotate, even with a hard push. This indicates that the direction of the force is also important to the rotation produced.

With these experiments in mind, we recognize that we must define a new quantity that describes the effectiveness of an interaction at producing rotation about a specific axis (in our examples, the axis was set by the line of the door hinges). This quantity is called torque.

Definition of Torque

Defining the torque resulting from a force requires two pieces of information:

1. The force applied (magnitude and direction).
2. The position (magnitude and direction) of the force's application with respect to the axis of rotation about which the torque is to be calculated.

The torque is most succinctly defined by using the vector cross product:

where τ is the torque, r is the position of the point of application of the force with respect to the axis of rotation, and F is the force.