Well... what is it that we are trying to teach? Are we teaching that
"anything goes" or are we teaching that one of the goals of learning
science is learning common practice so as to make it more likely that we
can communicate clearly.
If we are converting from i-j notation to r,theta notation, or
converting from i-j-k notation to r, theta,phi notation (or vice-versa)
there are some conventions we assume we are using. For example we
assume orthogonal axes and we even assume a right-handed coordinate
system.
If we are in 2-dimensions and converting from rectangular coordinates to
polar coordinates then the convention is than the angle is designated by
theta and theta is measured counterclockwise from the x axis, i.e. the i
direction. Continuing this, vectors having theta between 0 and 90
degrees are first quadrant, between 90 and 180 are second quadrant, and
so forth.
This is the convention in math books, physics books, high-school or
college, and also what practicing physicists use in publications, etc.
Why wouldn't we want students to understand this and use this
convention?
Yes... we also want to teach that physics is independent of the
coordinate system used. Yes, we don't really care which way the student
orients the axes as long as they maintain a right-handed system. But
once a standard coordinate system has been chosen and the orientation
has been chosen, we ought to follow conventions.
I do not totally disagree with Joel's assertion that we can accept any
convention as long as the student makes it clear what convention is
being used. Clarity is a very significant goal in our teaching. But if
clarity is what we are after, and assuming this implies accuracy and
ease of communication, then we also ought to teach (and expect students
to be able to use) the conventions that are fairly well established.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu