Moment of a force

The moment of a force, sometimes called torque by engineers, quantifies the ability of a force to generate rotational motion about an axis. The moment of a force can be calculated by multiplying the length of the line between the axis of rotation and the point of application of the force by the component of the force which is perpendicular to that line. In vector notation this is written, using the vector product, as:

${\vec {M}}={\vec {r}}\times {\vec {F}}$

where ${\vec {M}}$ is the moment of the force, ${\vec {r}}$ is the displacement vector from the axis of rotation to the point of application of the force and ${\vec {F}}$ is the force vector.

Since the moment of a force consists of the product between a distance and a force the S.I. units for moments are newton metres (Nm). These are dimensionally the same as the units for work done, joules (J), which is also formed from the multiplication of a force with a distance. However being two, distinct and separate physical concepts the units are always written as newton-metres and never as joules.

As a vector quantity the moment of a force has a direction as well as a magnitude. In most two-dimensional problems this is simply reduced to thinking of it as either a clockwise or anti-clockwise moment. However in three dimensions the moment vector is parallel to the axis of rotation. Empirically the direction of the vector is given by the right-hand rule: curl your fingers of your right hand about the axis of rotation in the direction of the force and your thumb will give the direction of the moment vector.