Sign Conventions

[Doug Craigen <dcc@ESCAPE.CA>]

Ludwik Kowalski wrote:
> As a student (and also when I started teaching) I accepted the
> convention that acceleration is positive while deceleration is
> negative. It prevented me from solving some kinematics
> problems in one step. The vertical throw problem, for example,

I have found what seems to be a simple matter, where to put a positive
sign and where to put a negative sign, to be one of the thorniest issues
in teaching many portions of first year physics.  There's the long list
of conventions in optics; there's work done "on" and "by"; there's
acceleration/decelleration and probably many more.  Throughout it all
there's the problem of double-negation in the wording and cases that
fall outside of the definitions (e.g. centripetal acceleration which
doesn't increase the velocity and could therefore just as easily be
called centripetal deceleration).

The double negation is the final straw for me.  Just when you thought
you had everything explained perfectly... they start doing some problems
out of the book.
"the rock is decellerating at a rate of -5 m/s^2"
So half of them put a=-5 and the other half put in -a since it is
decellerating and hence end up with +5.  If this was all there was to it
I could explain my way around it, but there's a good chance that the
next question will say something like "with a decelleration of 3
m/s^2".  Now the minus sign is supposed to be understood because it is
called decelleration.

And then there's the problem of g=+9.8 or g=-9.8 and what happens when
it is put into varrious equations.

I'm curious what others on this list have done.  My own solution has
been to play down sign conventions and to play up thinking about the
problem.  If something is supposed to be decellerating then make sure
that "a" is in the opposite direction as the initial velocity.  In fact,
this summer I didn't even mention the list of sign conventions for
optics - I just told them they could find a list in the text if they
wanted.  Instead I concentrated on the idea of real and virtual images
and explained the signs from there.

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Doug Craigen
          Latest Project - the Physics E-source
          http://www.dctech.com/physics/