The torques shown below are applied to a $108$ mm solid circular shaft through the four pulleys labeled $A,B,C$ and D $.$ Find the torque acting on each section of the shaft, the angle of twist in each section of the shaft, and the maximum shear stress.

As a first step, what is the polar moment of inertia of the shaft, $J,$ in units of $m{m}^4?$ Round your answer to four significant figures.