The circular disk of radius r is mounted on itsshaft which is pivoted at O so that it

Chapter 7, Problem 7/135

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The circular disk of radius r is mounted on its shaft which is pivoted at O so that it may rotate about the vertical \(z_{0} \text {-axis }\). 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 \(z_{0} \text {-axis }\). (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 \(2 \pi / \tau\).)