Physics:Line of action

Short description: Geometric representation of a force on an object

For the board game, see Lines of Action.

The line of action is shown as the vertical dotted line. It extends in both directions relative to the force vector, but is most useful where it defines the moment arm.

In physics, the line of action (also called line of application) of a force (F→) is a geometric representation of how the force is applied. It is the straight line through the point at which the force is applied, and is in the same direction as the vector F→. The lever arm is the perpendicular distance from the axis of rotation to the line of action.

Calculation of torque

For the simple geometry associated with the figure, there are three equivalent equations for the magnitude of the torque associated with a force $\overrightarrow{F}$ directed at displacement $\overrightarrow{r}$ from the axis whenever the force is perpendicular to the axis:

$\begin{array}{rl}||\overrightarrow{\tau }||& =||\overrightarrow{r}\times \overrightarrow{F}||\\ & =r{F}_{\perp }\\ & =r_{\perp }F\\ & =||rF\sin \theta ||,\end{array}$