Moment of Inertia of a Circular Disc

Consider an element of the arc length rdθ and width dr of the circular disc as shown in Figure 11.19. Now, the moment of inertia of the element about diametral axis x−x is given by,

Figure 11.19 Moment of Inertia of a Circular Disc about Its Diametral Axis 

I_XX = y² dA = (r sin θ)² r dθ dr = r³ sin² θ dθ dr

Now, moment of inertia of entire circle about diametral axis is given by