18 mm diameter, solid circular shaft is made of a metal with a shear modulus, G = 19,515 MPa. The shaft is 1.9 m long. If a torque of 9 Nm is applied to one end of the haft, what is the angle of rotation in the shaft in radians? Answer to 3 decimal places and assume the angle is in a positive direction.

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A flanged bolt coupling consists of eight d-mm diameter steel bolts on a bolt circle 267 mm in diameter, and four d-mm diameter steel bolts on a concentric bolt circle 190 mm in diameter. If the torque that can be applied is 8166 Nm without exceeding a shearing stress of 43.32 MPa in the bolts, what is the diameter of the bolts? Round off the final answer to two decimal places.

a: What is the magnitude of torque applied to the shaft? b: The magnitude of the Polar Moment of Inertia of the shaft cross-section? c: The magnitude of the shear stress at r=0in (center of shaft) is?