The Polar Coordinates are defined as two-dimensional co-ordinate system, used to locate arbitrary Point positions lying on the circumference of a single two-dimensional plane like a Circle and situated at a particular distance from a fixed point.
Their use in this context is where the phenomenon being considered is essentially related to the direction and the length from a Centre point of the plane.
Moreover, many physical systems—such as those concerned with objects moving around a central point or with phenomena originating from a central point—are simpler and more spontaneous to model using polar coordinates.
The initial incentive taken in the field of explaining the applications of Polar Coordinates was the study related to circular and orbital motion.
Navigation can also be a noticeable application of Polar coordinates, as we consider the direction of travel can be given as an angle and distance from the object being considered. Thus the destination can be come to know by knowing the navigation direction of the Polar coordinates.
According to the conventions that are followed by the aircrafts using the polar coordinates the magnetic north can be understood as moving in a direction along 360 and the rest directions are specified by 90, 180 and 270 respectively.
Another application of Polar Coordinate Systems is modelling which can be used to display radial Symmetry providing natural settings for the polar coordinate system, with the central point acting as the pole.
For Example we can consider the following:
Groundwater flow equation applied to radically symmetric wells.
Systems including gravitational fields with a radical force also have a good usage of the polar coordinate system.
Modelling with polar coordinates also cover their usage in asymmetric systems like we can get a proportionate response to an incoming sound signal from a given direction is usually found in microphone's pickup pattern.