from a disk of radius R,a concentric circular portion of radius r is cut out so as to leave an annular disc of mass M . the moment of inertia of this annular disc about the axis perpendicular to its plane and passing through its centre of gravity is
To calculate the moment of inertia of the annular disc, we can use the parallel axis theorem. The moment of inertia of an annular disc is given by the formula:
I = (1/2) * M * (r1^2 + r2^2)
where M is the mass of the annular disc, r1 is the inner radius of the annular disc, and r2 is the outer radius of the annular disc.
In this case, the radius of the original disk is R, and a concentric circular portion of radius r is cut out. Therefore, the inner radius of the annular disc is R - r, and the outer radius is R.
Substituting these values into the formula, we get:
I = (1/2) * M * ((R - r)^2 + R^2)
So, the moment of inertia of the annular disc about the axis perpendicular to its plane and passing through its center of gravity is (1/2) * M * ((R - r)^2 + R^2).