Problem $1$: A circular shaft is used to transmit power from a

motor to a machine. The following are some scenarios of loads,

geometry, and material.

a$.(4$ points$)$ Given L$1,$ G$1,$ and M$1,$ find the minimum

required diameter that will ensure a factor of safety of $6$

against torsional shear failure. All other failure modes may

be ignored.

b$.(8$ points$)$ Given L$1,$ G$2,$ and M$2,$ what is the factor of

safety guarding the design against torsional shear failure?

All other failure modes may be ignored.

c$.(8$ points$)$ Given L$2$ and G$2,$ find a suitable AISI steel grade

that would ensure a factor of safety of $8$ against torsional

shear failure. All other failure modes may be ignored.