$3\mathrm{.}9-12$ A heavy flywheel rotating at $n$ revoluti$$ns per minute is rigidly attached to the end of a shaft of diameter $d($see figure$).$ If the bearing at A suddenly freezes, what will be the maximum angle of twist $$ 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.