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Circle Rolling Around A Circle

Updated: Aug 2, 2023

As shown in below picture, Circle A (with radius r=1cm) rolls without slipping around Circle B (with radius R=3cm) on a horizontal plane. If the center of mass of Circle A completes one trip around Circle B, coming back to its starting point, how many times will Circle A have rotated about its own center of mass? Assume that the circles are homogeneous, so the center of mass of each circle is located at its corresponding geometric center, and the center of Circle B is fixed at its location and Circle B is not rotating with respect to its own center of mass.

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