S.T. the time rate of the total angular momentum of a system of particles about a point is equal to the sum of the external torques acting on the system taken about the same point.

Explanation

Net angular momentum `=vecL=vecL_1+vecL_2+………vecL_n=sumvecr_ixxvecp_i`
Now `(dvecL)/(dt)=sumd/(dt)vecr_ixxvecF_i=sumvecr_ixxvecF_i` where `(dvecp)/(dt)=vecF=sumtau_i` but `vectau_("int")=0` and `sumvectau_i=vectau_("int")+vectau_("ext")`
`:. (dvecL)/(dt)=vectau_("ext")`