Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_146

2/146 In the design of an amusement-park ride, the cars are attached to arms of length \(R\) which are hinged to a central rotating collar which drives the assembly about the vertical axis with a constant angular rate \(\Omega = \dot{\theta}\). The cars rise and fall with the track according to the relation \(z = (h/2)(1 - \cos 2\theta)\). Find the \(R\)-, \(\theta\)-, and \(\phi\)-components of the velocity \(\mathbf{v}\) of each car as it passes the position \(\theta = \pi/4\) rad.