고체역학 (Gere) — Torsion: Problem 3.9-12

3.9-12 A heavy flywheel rotating at \( n \) revolutions per minute is rigidly attached to the end of a shaft of diameter \( d \) (see figure). If the bearing at \( A \) suddenly freezes, what will be the maximum angle of twist \( \phi \) of the shaft? What is the corresponding maximum shear stress in the shaft? (Let \( L = \) length of the shaft, \( G = \) shear modulus of elasticity, and \( I_m = \) mass moment of inertia of the flywheel about the axis of the shaft. Also, disregard friction in the bearings at \( B \) and \( C \) and disregard the mass of the shaft.) Hint: Equate the kinetic energy of the rotating flywheel to the strain energy of the shaft.