Angles of Twist  
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Free-Body diagram of the shaft A B C which cuts through A B shows the torques 600 Newton meter, 200 Newton meter acting on B and C, and a positive internal torque T subscript 1 acts on A B towards A. The length of A B is 100 millimeters, B C is 300 millimeters. The internal torque at A B is 400 Newton meter. A positive internal torque T subscript 2 acts on B C towards B. The internal torque at B C is negative 200 Newton meter. Tau at A B is 130.4 mega Pascal and Tau at B C is negative 65.2 mega Pascal.

The angle of twist in shaft segment (1) between A and B is:

ϕ1=T1L1JG=(400 N-m)(100 mm)(1,000 mm/m)(38,350 mm4)(66 GPa)(1,000 MPa/GPa)=+0.0158 rad

The twist angle in shaft segment (2) between B and C is:

ϕ2=T2L2JG=(-200 N-m)(300 mm)(1,000 mm/m)(38,350 mm4)(66 GPa)(1,000 MPa/GPa)=-0.0237 rad