AP Physics C: Mechanics 5.3 A Identify the Torques Exerted on a Rigid System Questions

A solid uniform disk is supported by a vertical stand. The disk is able to rotate with negligible friction about an axle that passes through the center of the disk. The mass and radius of the disk are given by $M_{\mathrm{d}}$ and R, respectively. The rotational inertia of the disk is $I_{\mathrm{d}}=\frac{1}{2} M_{\mathrm{d}} R^{2}$. A string of negligible mass is draped over the disk and attached to the top of the disk at point P. One end of the string is connected to an unstretched ideal spring of spring constant k, which is fixed to the ground as shown in Figure 1.
A block of mass $m_{\mathrm{B}}$ is then attached to the string on the right side of the disk. The block is slowly lowered until the spring-disk-block system reaches equilibrium, as shown in Figure 2. In this equilibrium position, the disk has rotated clockwise through a small angle $\theta$.
Give all algebraic answers in terms of $M_{\mathrm{d}}, R, k, \theta$, and physical constants, as appropriate.

The disk is adjusted on the support so that the axle does not pass through the center of mass of the disk. The block is again hung on the right side of the disk and the spring-disk-block system comes to equilibrium, as shown in Figure 3. The axle does not exert a torque on the disk. For each force on the disk, indicate whether the magnitude of the torque about the axle caused by that force increases, decreases, or stays the same relative to part (b).