The relation between torque and angular acceleration

Let us consider a rigid body rotating about a fixed axis X0X′ with angular velocity ω (Fig. below).
The force acting on a particle of mass m1 situated at A, at a distance r1, from the axis of rotation = mass × acceleration

Relation between torque and angular momentum
The angular momentum of a rotating rigid body is, L = I ω Differentiating the above equation with respect to time,
dL/dt = I(dω/dt) = Iα
where α = dω /dt angular acceleration of the body.
But torque τ = Iα
Therefore, torque τ = dL/dt
Thus the rate of change of angular momentum of a body is equal to the external torque acting upon the body.