The rotational inertia of any flat object about an axis perpendicular to the object is equal to the sum of the rotational inertias about two mutually perpendicular axes in the plane of the object, if all three axes pass through a common point. Using this "perpendicular-axis theorem," determine \((a)\) the rotational inertia of a uniform hoop of inertia \(m\) and radius \(R\) about a diameter of the hoop, and \((b)\) the rotational inertia of a uniform square sheet of inertia \(m\) and side length \(a\) about a line drawn from the midpoint of one edge to the midpoint of the opposite edge.