Problem $2(20$ points$)$:

A two$-$segment shaft is used to transmit power at constant speed through the pulleys shown in

the figure. Power is input to the shaft at B through a torque of $T_B=225N*m.$ A torque

of $T_A=70N*m$ is removed from the shaft at A $,$ and a torque of $T_C=155N*m$ is removed from the

shaft at C $.$ The external torques act in the directions indicated in the figure. Both shaft segments

are made of phosphor bronze $[G=42$GPa $]$ and both segments are solid shafts. Segment $(1)$ has a

diameter of $d_1=25mm$ and a length of $L_1=305mm.$ Segment $(2)$ has a diameter

of $d_2=30mm$ and a length of $L_2=925mm.$ Determine the rotation angle of pulley C relative to

pulley A$.$