nLab torque

Idea

The moment of a force.

 Definition

For point particles

Given a point particle $P$ in an Euclidean space $\mathbb{R}^n$, an associated lever arm vector $\overrightarrow{r}:\mathbb{R} \to \mathbb{R}^n$ and a force $\overrightarrow{f}:\mathbb{R} \to \mathbb{R}^n$ acting on $P$, the torque or moment of a force $M$ is the wedge product of the lever arm vector and the force:

$$M(t) = \overrightarrow{r}(t) \wedge \overrightarrow{f}(t)$$

Thus, torque is a bivector.

See also

• areal velocity

• angular momentum

• moment of inertia

References

See the references at differential geometry of curves and surfaces.

See also:

• Wikipedia, Torque