# What is the difference between 'torque' and 'work'?

Oct 2, 2017

Torque

Torque is defined as the moment of force i.e. the rotating effect produced by a given force.

It is essentially the rotational analogue of force.

For a force $\vec{F}$ acting on a point $\vec{r}$, the torque generated about the origin is,

$\vec{N} = \vec{r} X \vec{F}$

Work

On the other hand, the work done by a force $\vec{F}$ in displacing an object through a displacement $\mathrm{dv} e c r$ is defined as,

$\mathrm{dW} = \vec{F} \cdot \mathrm{dv} e c r$

Therefore, for a displacement from $a$ to $b$, the work done by the force $\vec{F}$ is,

${W}_{a b} = {\int}_{a}^{b} \vec{F} \cdot \mathrm{dv} e c r$