What is torque? Explain the torque acting on a particle.

Explanation

The role of torque in rotational motion is similar to the role of force in transaction motion.

As shown in the figure a force `vecF` is acting on a particle P having position vector `vecr` w.r.t. the origin O. The angle between `vecr and vecF` is `theta`. Here P need not be a particle of a rigid body.
The vector product of `vecr and vecF` is defined as the torque `vectau` acting on the particle w.r.t. origin O.
`therefore vectau=vecrxxvecF`
and magnitude `tau=rFsintheta`
where `|vecr|=rand|vecF|=F`
Also, the angle between `vecr and vecF` is `theta`
`therefore tau=rFsintheta=(rsintheta)F orr(Fsintheta)`
`therefore tau=r_(_|_)F[because r_(_|_)=rsintheta]or`
`tau=rF_(_|_)[because F_(_|_)=Fsintheta]`
where `tau` = (Force) (perpendicular distance of the line of action of force from origin) or `tau` = (magnitude of position vector) `xx` (component of force in the direction perpendicular to position vector)
`therefore tau` = moment of force w.r.t. point O.