Question

1. Show that the rate of change of the total angular momentum of a system of particles is equal to the resultant torque exerted by all external forces which act on the system. 

Answer 1

$$m\frac{d\vec{v}}{dt}\times\vec{l}=\vec{F}\times\vec{l} \\\frac{d(m\vec{v}\times\vec{l})}{dt}=\vec{\tau}\\\frac{d\vec{L}}{dt}=\vec{\tau}$$