Problem $4(4$ points$)$: A $2-$hp electric motor runs at $1800re\frac{v}{m}in$ in the clockwise direction, as viewed from the positive $x$ axis. Keyed to the motor shaft is an $18-$tooth helical pinion having a normal pressure angle of $20,$ a helix angle of $30,$ and a normal diametral pitch of $12$ teeth$/$in$.$ The hand of the helix is shown in the figure.

a$.$ Determine the various forces acting on the pinion.

b$.$ Determine bearing reactions at A and $B$ if the thrust should be taken out at $A.$

For all calculations, please draw proper FBDs$.$