Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 41

41 Figure 11-39 shows a rigid structure consisting of a circular hoop of radius \(R\) and mass \(m\), and a square made of four thin bars, each of length \(R\) and mass \(m\). The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of \(2.5\text{ s}\). Assuming \(R = 0.50\text{ m}\) and \(m = 2.0\text{ kg}\), calculate (a) the structure’s rotational inertia about the axis of rotation and (b) its angular momentum about that axis.