Physical interpretation of the definition of torque :

Explanation

As shown in the figure a force `vecF` is acting on a particle P of rigid body.
Force `vecF` is taken in the plane perpendicular to the axis of rotation.
The axis is perpendicular to the plane of the figure and passing through point O. The position vector of P w.r.t. the centre of its circular path is `vecr`. The angle between `vecF and vecr` is `theta`.
To examine the effectiveness of the force in produing rotational motion, `vecF` can be resolved into two mutually perpendicular components.
(1) Component of `vecF` parallel to `vecr` is `Fcostheta` which does not produce rotational motion.
(2) Component of `vecF` perpendicular to `vecr` is `Fsintheta`. Which can produce the rotational motion. If F and/or `theta` large, `vecF` will be more effective. Moreover if the position vector `vecr` of the point of application of the force `vecF` is large, the effectiveness of the force in producing rotational motion is more.
Thus the quantity responsible for producing rotational motion is not only `vecF` but `rFsintheta`. If can be written in vector form as under.
`vectau = vecr xx vecF`
Torque is the measure of effectiveness of force in producing rotational motion.