Determine the moment of inertia of a uniform square plate having mass m and edge a about one of its diagonals.

Step-by-step solution

Let the square plate lie in the xy -plane with its center at the origin and its edges parallel to the x and y axes. The moment of inertia of the square plate about the x -axis passing through its center is I_x = ma^2 12 . The moment of inertia of the square plate about the y -axis passing through its center is I_y = ma^2 12 . By the perpendicular axis theorem, the moment of inertia about the z -axis passing through the center and perpendicular to the plane is I_z = I_x + I_y = ma^2 12 + ma^2 12 = ma^2 6 . Let the t