Question

State the case of many particle system of Torque and angular momentum.

Answer 1

Let there be many particles having momenta

Now it arises due to two types of sources-particles within the system boundary and the particles outside the boundary of the system. Let be the force exerted by internal particles.We call it internal force.

Let vector F_iext be the force exerted by external particle; we call it external force. Then 

It is experimentally found that internal torque can’t change angular momentum of the system.

The rate of change of angular momentum of a system of particles about a point in an internal reference frame is equal to net external torque about the same point. 

Taking Z-component of the above relationship (equation -iv) we get

The external torque acting on a rigid body about an axis is equal to the product of moment of inertia and angular acceleration about the same axis.