Line of action

For the simple geometry associated with the figure, there are three equivalent equations for the magnitude of the torque associated with a force \vec F directed at displacement \vec r from the axis whenever the force is perpendicular to the axis: :\begin{align} & = rF_\perp \\ & = r_\perp F \\ & = ||r F \sin\theta|| \,, \end{align} where \vec r\times\vec F is the cross-product, F_\perp is the component of \vec F perpendicular to \hat r, r_\perp is the moment arm, and \theta is the angle between \vec r and \vec F. == References ==