Problem 1.240

Demonstrate that in the case of a thin plate of arbitrary shape there is the following relationship between the moments of inertia: \(I_{1}+I_{2}=I_{3},\) where subindices \(1,2,\) and 3 define three \(\mathrm{mu}-\) tually perpendicular axes passing through one point, with axes 1 and 2 lying in the plane of the plate. Using this relationship, find the moment of inertia of a thin uniform round disc of radius \(R\) and mass \(m\) relative to the axis coinciding with one of its diameters.