1. A hollow aluminum tube has an outside diameter of 1 in. and an inside diameter of 0.50 in. The tube is subjected to a maximum shear stress of 7000 psi. Calculate the angle of twist per foot of length.
2. A solid steel shaft is to resist a torque of 9000 lb-in. The angle of twist is not to exceed 0.12° per foot of length, and the allowable shear stress is 8000 psi. Calculate the required diameter of the shaft and select an appropriate diameter to use.