A gear train is composed of four gears, where gears A and B are on the same shaft. Gear A has 60 teeth, gear B has 36 teeth, gear C has 48 teeth, and gear D has 12 teeth. If a torque of 0.961 N·m is applied to gear D, determine the torque at gear A.

A torque of 26 lb·in. is applied to one end of a 7-in.-long composite shaft that consists of two polymer tubes. The outer tube has a polar moment of inertia of 0.037 in.4 and a shear modulus of 170 ksi. The inner tube has a polar moment of inertia of 0.00779 in.4 and a shear modulus of 180 ksi. Determine the magnitude of the torque produced in the inner tube.

A dump truck axle with a diameter of 1.675 in. and a length of 37.3 in. failed when the shear stress reached 89 ksi on the outer surface. The shear modulus of the steel is G = 11,100 ksi. Assuming the shaft did not yield prior to failure, determine the angle of twist of the axle when it failed.

A dump truck axle with a diameter of 1.621 in. and a length of 38.0 in. failed when the shear stress reached 80 ksi on the outer surface. The shear modulus of the steel is G = 11,300 ksi. Assuming the shaft did not yield prior to failure, determine the angle of twist of the axle when it failed.

A dump truck axle with a diameter of 1.690 in. and a length of 37.9 in. failed when the shear stress reached 73 ksi on the outer surface. The shear modulus of the steel is G = 11,700 ksi. Assuming the shaft did not yield prior to failure, determine the angle of twist of the axle when it failed.

A load of P = 14 N is applied to a hex wrench that has lengths a = 29 mm and b = 87 mm. Determine the torque applied to the set screw.

A load of P = 20 N is applied to a hex wrench that has lengths a = 28 mm and b = 109 mm. Determine the torque applied to the set screw.

A dump truck axle with a diameter of 1.620 in. and a length of 37.8 in. failed when the shear stress reached 79 ksi on the outer surface. The shear modulus of the steel is G = 11,300 ksi. Assuming the shaft did not yield prior to failure, determine the angle of twist of the axle when it failed.

The solid circular steel shaft of a screwdriver is subjected to a pure torque of T = 23 lb·in. The shaft has a diameter of 0.234 in. and a length of L = 3.75 in. The shear modulus of the steel is G = 11,300 ksi. Determine the magnitude of the angle of twist of the shaft in degrees.

A steel [E = 30,300 ksi, G = 11,900 ksi] socket extension (2) has a diameter of 0.32 in. and a length of L = 2.3 in. It connects socket (3) to ratchet handle (1) which is 4.9 in. long. If a perpendicular force of 7.0 lb is applied to the end of the ratchet handle, determine the maximum shear stress in the socket extension.