Problem $2$: There is a torque $T=2000lb-ft$ on the cylinder shaft as shown below. There is also a moment on the shaft such that ${}_x=+1200$ and ${}_y=+1000$ psi. The solid shaft radius is $2^{\text{'}\text{'}}.$ Determine:

a$)$ Draw the element and label it correctly.

b$)$ Determine the minimum and maximum normal stresses and maximum shear stress with the equations. Also find the angles of rotation for both.

c$)$ Now find the minimum and maximum normal stresses and maximum shear stress with Mohr's circle. Also find the angles of rotation for both. Draw the elements.

Please use the graph paper to draw Mohr's circle close to scale. Show all work.