## Task

The forces F_{1} and F_{2} are located in the x-y plane. Calculate the resulting moment for both forces combined at the origin.

F_{1} = 20 N, F_{2} = 30 N

x_{1} = 1 m, x_{2} = 2 m, y_{1} = 1 m, y_{2} = 2 m

## Solution

The following video is in german language.

We assume left-turning moments to be positive. The resulting moment is given by:

\[ \require{cancel} \] \[ \newcommand{\myvec}[1]{{\begin{pmatrix}#1\end{pmatrix}}} \]\[\tag{1} M_0 = F_1 \cdot x_1 - F_2 \cdot y_1 \]

\[\tag{2} M_0 = 20 N \cdot 1 m - 30 N \cdot 1 m \]

\[\tag{3} M_0 = -10 N m \]

## Annotations

The assumption of the left-turning positive moments results from the right-hand-rules. The z-axis of the coordinate system points to the viewer, this leads to left-oriented positive moments.