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A baby-swing motor provides 0.32 W at 5,700 rpm to a shaft that has a diameter of 2.03 mm and a length of 14.1 mm. Determine the maximum shear stress in the shaft.

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 1.93 N·m is applied to gear A, determine the torque at gear D.

A steel [E = 30,200 ksi, G = 11,800 ksi] socket extension (2) has a diameter of 0.48 in. and a length of L = 1.8 in. It connects socket (3) to ratchet handle (1) which is 7.3 in. long. If a perpendicular force of 19 lb is applied to the end of the ratchet handle, determine the maximum shear stress in the socket extension.

A dump truck axle with a diameter of 1.78 in. and a length of 38 in. failed while transmitting a power of 485 hp and a torque of 8,030 lb-ft. At what speed was the axle spinning when it broke?

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 2.25 N·m is applied to gear A, determine the torque at gear D.

A steel [E = 30,500 ksi, G = 11,600 ksi] socket extension (2) has a diameter of 0.50 in. and a length of L = 1.3 in. It connects socket (3) to ratchet handle (1) which is 7.5 in. long. If a perpendicular force of 11 lb is applied to the end of the ratchet handle, determine the maximum shear stress in the socket extension.

The solid circular steel shaft of a screwdriver is subjected to a pure torque of T = 16 lb·in. The shaft has a diameter of 0.241 in. and a length of L = 4.50 in. The shear modulus of the steel is G = 11,000 ksi. Determine the magnitude of the angle of twist of the shaft in degrees.

A solid constant-diameter shaft is subjected to the torques shown. Determine the absolute value of the internal torque in segment (2) of the shaft. Assume that TA = 12.4 N·m, TB = 31.6 N·m, TC = 17.4 N·m, TD = 38.9 N·m, and TE = 40.7 N·m.

Please complete the following questions and upload your written solutions as a single file. If you are writing on a document or paper different than the provided pdf, please clearly indicate the question number and answer for each question, and include your name. Your work will be graded just as much (if not more) as your final answer. That includes cleanliness, legibility, and organization of argument. Correct answers with little to no work will not be given full credit.   Math_2063___Exam_1.pdf

The same torque is applied to three socket extensions. They have the same length and modulus of rigidity but different diameters. Which one will have the largest polar moment of inertia?