Moments

Rigid bodies have size. Therefore, forces applied at locations other than the center of mass, induce a moment about the center of mass. The moment induced by a force about an arbitrary point P is given by ...

M_P = r x F

Presented below are three methods that may be used to calculate the moment induced by a force F about reference point O. The distance of the point of force application from point O is r.

Perpendicular-moment arm method

This method uses the perpendicular component of either force F or position vector r to calculate the moment. The direction of the moment is determined by the right-hand rule.

M_O = F_⊥r = Fr_⊥

Force-component method

This method uses the x- and y-components of the force and position vector to calculate the moment. The direction of the moment, that is, whether the signs in the following equation are positive or negative is determined by the right-hand rule.

M_O = ±r_xF_y ± r_yF_x

Cross-product method

If the other two methods are inconvenient to use or you are working in 3-D, the most general way of calculating a moment is to use the cross product.

M_O = r x F