In this problem, you are to derive the perpendicular-axis theorem for planar objects, which relates the moments of inertia about two perpendicular axes in the plane of Figure to the moment of inertia about a third axis that is perpendicular to the plane of figure. Consider the mass element dm for the figure shown in the xy plane. 

(a) Write an expression for the moment of inertia of the figure about the z axis in terms of dm and r. 

(b) Relate the distance r of dm to the distances x and y, and show that I_z = I_y + I_x. 

(c) Apply your result to find the moment of inertia of a uniform disk of radius R about a diameter of the disk.

Transcribed Image Text:

x dm