What is the purpose...

ME_student

of converting a rectangular coordinate to a polar coordinate and changing polar to rectangular?

Where would they use this in engineering?

algebrat

In physics, depending on the problem, it is much better to use rectangular coordinates in some problems, polar coordinates in others.

For instance, if you open up most college level physics, the first few chapters are mostly problems done in rectangular coordinates (though sometimes polar is a natural way to describe a physical setup, but often the math is better done in rectangular coordinates). Then maybe halfway through the course, they introduce rotational problems. We usually treat applications in rectangular or polar depending on the physical setup, and the biggest reason is it makes it much more straightforward to solve these equations in the coordinates that fit with the situation.

ME_student

Okay, thanks.

TheShrike

As a practical example, consider a central potential [itex]V(s)[/itex], which depends only on the distance from the origin.

In Cartesian coordinates [itex](x,y,z)[/itex] we have

[itex]s=\sqrt{x^2+y^2+z^2}[/itex]

whereas in spherical polar coordinates [itex](r,\theta,\phi)[/itex] we have

[itex]s=r[/itex]

Which would you prefer to integrate? ;)

HallsofIvy

In other words, problems with circular symmetry will typically be simpler in polar coordinates while problems with symmetry about a line will be simpler in Cartesian coordinates.