$2.$ A shaft carries a torque $($twist$)$ of $1,500$ N$$m$,$ and the shaft has a diameter of $15$ mm$.$

a$.$ Look up the formula and find the polar moment of inertia J for this shaft.

b$.$ What is the maximum torsional shear stress due to this load? Is the maximum

shear stress on the surface or at the center of the shaft?

c$.$ This torque is applied over a distance along the shaft of $50$ mm$.$ What is the

angular deflection? Give your answer in both radians and degrees.

d$.$ They will need the polar moment