The drive roller rotates on a $2\mathrm{.}000-$inch diameter shaft on two outboard bearings attached to the frame of the conveyor system. A $2-$inch shaft extends beyond the bearing a total of $6\mathrm{.}00$ inches to allow a drive mechanism. To drive this shaft, a pulley or sprocket must be attached to the end of the shaft. Assuming the drive component $($pulley or sprocket$)$ is permitted a diameter of no more than $15$ inches to allow guarding and clearance.

Find all forces, torques, and moments on the shaft. Design and analyze a square key to drive the shaft showing all calculations to transmit the torque generated.