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

The circular motion is usually analyzed by using the polar coordinates . The transformation between Cartesian coordinates (x,y) and polar coordinates is


where basically  corresponds to the distance between the object and the origin of the axes (0,0) while  is the angle which gives the direction.

The main advantage of the polar coordinates is that when analyzing a circular motion, the radius  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 .

Pe = 1/2k(x)^2  and .05n/m = .05x10^-9m = x