The circular disk of radius r is mounted on its shaft which is pivoted at O so that it may rotate about the vertical z₀-axis. If the disk rolls at constant speed without slipping and makes one complete turn around the circle of radius R in time τ, determine the expression for the absolute angular velocity w of the disk. Use axes x-y-z which rotate around the z₀-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 2π/τ.)

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-- R