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Moment of inertia of a uniform disc
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The Moment of inertia of a uniform disc of mass m, and radius r is given by the formula: 
Let m=mass of a uniform disc,
R=radius of the disc.
Let the axes pass through the mass centre of gravity. The thickness of the disc is negligible and it can be considered as 2D or plane.The moment of inertia is firstly calculated for a small amount of mass of dm in the plane taken radially at a distance which is negligible for all points of dm. The dr is the inner distance of dm on the axis of R. As the area is rdx where dx=the angle created by the dm. The Z axis is perpendicular on the plane.So the cylindrical coordinates (r,x) can be used to integrate to measure the whole moment.
The area element dA is the product of the length rdx and the radial width dr.
As the disc is uniform the density is same and for that the expression becomes