Make your life simple!
In tackling a physics problem it is important to choose a coordinate system that is tailored to its ‘geometry’ or ‘symmetry’.
To describe motion on an inclined plane (left) we would generally use cartesian coordinates, x and y, along and perpendicular to the plane.
To describe the motion of a body experiencing some radial (centripetal) force (right) we would generally use cylindrical coordinates r and φ describing the radial distance from the force centre and the angular position of the object.
Choosing the coordinate system wisely can greatly simplify the problem.
Note, however, that we must (in general) choose coordinate axes that constitute an inertial reference frame: this is the key precondition for Newton’s 2nd law (Key Point 2.2).