Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_123

3/123 The two wheels consisting of hoops and spokes of negligible mass rotate about their respective centers and are pressed together sufficiently to prevent any slipping. The 3-lb and 2-lb eccentric masses are mounted on the rims of the wheels. If the wheels are given a slight nudge from rest in the equilibrium positions shown, compute the angular velocity \(\dot{\theta}\) of the larger of the two wheels when it has revolved through a quarter of a revolution and put the eccentric masses in the dashed positions shown. Note that the angular velocity of the small wheel is twice that of the large wheel. Neglect any friction in the wheel bearings.