deduce the relation between torque and angular momentum

Dear Student
Linear momentum = mass * velocity

Similar to this, angular momentum = angular mass (moment of inertia) * angular velocity

So, L = I ω

Differentiating this with respect to time, dL / dt = d (I ω) / dt

Moment of inertia is irrespective of the time. Only angular velocity is dependent upon time.

So, dL / dt = I dω/dt

Change of angular velocity with time = angular acceleration.

So, dL / dt = I α

But torque = I α (SeeVishakh Rajendran's answer to What is the relationship between torque and angular acceleration?)

torque = I α = dL / dt

the rate of change of angular momentum = Torque acting on the body


Thanks