Eind the products of inertia of a rod?

The products of inertia for a rod depend on its orientation and axis of rotation. For a thin, uniform rod of length ( L ) about its center and perpendicular to its length, the products of inertia ( I_{xy} ) are zero because the mass is symmetrically distributed about both axes. If the rod is oriented along the x-axis, the product of inertia about the x and y axes remains zero, since there are no off-diagonal mass distributions. Thus, for a rod, ( I_{xy} = 0 ).