Total external torque acting on a system of particles:

If \( \vec{F_i} \) be the external force acting on ith particle of mass \( m_i \) having position vector \( \vec{r_i} \) with respect to the origin, then the moment of force \( \vec{F_i} \) or torque about that origin is \( (\vec{r_i}\times\vec{F_i}) \). So the total external torque acting on a system of n particles is given by,

\( \displaystyle{\vec{\tau}=\sum_{i=1}^{n}(\vec{r_i}\times\vec{F_i})} \)