Obtain the relation between angular momentum of a particle and torque acting on it.

Explanation

By definition of angular momentum of a particle, `vecl=vecrxxvecp`
Differentiating this equation w.r.t. time t,
`(dvecl)/(dt)=vecrxx(dvecp)/(dt)+(dvecr)/(dt)xxvecp`
But, `(dvecp)/(dt)` = rate of change of linear momentum = force `vecF and (dvecr)/(dt)=vecv`
`therefore (dvecl)/(dt)=vecrxxvecF+vecvxxvecp`
But as `vecv and vecp` are in the same direction,
`vecvxxvecp=0`
`therefore (dvecl)/(dt)=vecrxxvecF=vectau`
Thus, ..the time rate of change of angular momentum is equal to the torque...