Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_147

6/147 The device shown is a simplified model of an amusement-park ride in which passengers are rotated about the vertical axis of the central post at an angular speed \(\Omega\) while sitting in a pod which is capable of rotating the occupants 360° about the longitudinal axis of the connecting arm attached to the central collar. Determine the percent increase \(n\) in angular velocity between configurations (a) and (b), where the passenger pod has rotated 90° about the connecting arm. For the model, \(m = 1.2 \text{ kg}\), \(r = 75 \text{ mm}\), \(l = 300 \text{ mm}\), and \(L = 650 \text{ mm}\). The post and connecting arms rotate freely about the \(z\)-axis at an initial angular speed \(\Omega = 120 \text{ rev/min}\) and have a combined mass moment of inertia about the \(z\)-axis of \(30(10^{-3}) \text{ kg}\cdot\text{m}^2\).