Question

describe the coordinate system that is usually chosen for analyzing circular motion and state at least one advantages for this choice.

Answer 1

The circular motion is usually analyzed by using the polar coordinates $(\rho, \theta)$. The transformation between Cartesian coordinates (x,y) and polar coordinates is
$x= \rho cos \theta$
$y= \rho \sin \theta$
where basically $\rho$ corresponds to the distance between the object and the origin of the axes (0,0) while $\theta$ is the angle which gives the direction.

The main advantage of the polar coordinates is that when analyzing a circular motion, the radius $\rho$ is a constant, since the object is moving on a circular path, and so it is possible to describe the motion of the object by specifying only the angle $\theta$.