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

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Answer 1 · 2017-10-02T12:52:47

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 $\to F$ $vec F$ acting on a point $\to r$ $vec r$ , the torque generated about the origin is,

$\to N = \to r X \to F$ $vec N = vec r X vec F$

On the other hand, the work done by a force $\to F$ $vec F$ in displacing an object through a displacement $d \to r$ $dvecr$ is defined as,

$d W = \to F \cdot d \to r$ $dW = vec F*dvecr$

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

$W_{a b} = \int_{a}^{b} \to F \cdot d \to r$ $W_(ab) = int_a^b vec F*dvecr$