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Theory of circular motion is described at many references, such as https://en.wikipedia.org/wiki/Circular_motion. In this case, a body performs circular motion on a stationary path. For example, a car moving along a circular road. For this case, we have the equations of motion.

But what happens when a body performing circular motion on a body in circular motion? For example, a large disc is in circular motion and a small autonomous car performing circular motion. And these motions are observed by a stationary observer. A similar case would be a car performing circular motion on the earth's equator and a stationary observer outside earth.

Is this related to inertial frame of reference? Your comments are appreciated.

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Not sure what you are asking but here goes. With respect to observer on ground car would seem to rotate with $\vec{\omega_{car}}+\vec{\omega_{disc}}$, where angular velocity is the vector summation, whereas it remains for the disc with respect to ground observer $\vec{\omega_{disc}}$

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