Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_119

7/119 The circular disk of radius \(r\) is mounted on its shaft, which is pivoted at \(O\) so that it may rotate about the vertical \(z_0\)-axis. If the disk rolls at constant speed without slipping and makes one complete turn around the circle of radius \(R\) in time \(\tau\), determine the expression for the absolute angular velocity \(\omega\) of the disk. Use axes \(x\)-\(y\)-\(z\) which rotate around the \(z_0\)-axis. (Hint: The absolute angular velocity of the disk equals the angular velocity of the axes plus (vectorially) the angular velocity relative to the axes as seen by holding \(x\)-\(y\)-\(z\) fixed and rotating the circular disk of radius \(R\) at the rate of \(2\pi/\tau\).)