Circular motion on rotating body

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.

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 $\vec{\omega_{disc}}$