Moment of Force

Describes the "turning effect" a force exerts on a rigid body

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

To determine the component of a certain moment $M_{0}$ about a certain axis $β$ .
$M_{β} = (\vec{A} \times F \cdot n_{β}) n_{β}$

The component of moment $M_{0}$ perpendicular to a certain axis $β$ is then:
$M_{β ⊥} = M_{0} - M_{β}$ .

Definition

Varignon's theorem states that Moment of Force $M O$ about point $O$ is equal to the sum of the moments of the components of the force about the same point.

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$\vec{M_{O}} = \hat{r_{O A}} \times \vec{R} = \hat{r_{O A}} \times (\vec{F_{1}} + \vec{F_{2}}) = \hat{r_{O A}} \times \vec{F_{1}} + \hat{r_{O A}} \times \vec{F_{2}}$