Given: A solid shaft with two gears, A and B, is driven by a motor. Gears A and B apply torques to the shaft of T_A = 250 lb-in. and T_B = 300 lb-in as shown. The shaft has the following dimensions: diameter, D = 0.5 in.; L₁ = 6 in.; and L₂ = 10 in. The Shear Modulus of the shaft is G = 10 Msi.

Req'd: Determine the Polar Moment of Inertia of the shaft J.