Question
Derive an expression for torque in terms of moment of inertia of body and its angular acceleration.
Solution
Consider a rigid body rotating about XY-axis under the action of external torque τ.
As a result the body possesses the angular acceleration ‘α’ about the axis of rotation.
All the constituent particles possess the same angular acceleration but the linear acceleration of different particles will be different.
The acceleration of ith particle is,
ai = ri α
The magnitude of external force on ith particle will be,
Fi =mi ai = mi ri α
This force on the ith particle produces the turning effect.
The magnitude of torque on this particle is equal to the product of force and the perpendicular distance from the axis of rotation to the line of action of force.
Therefore total torque acting on rigid body is, 
