Re: Being careful with dimensions (was Re: i,j,k things)

[Michael Edmiston <edmiston@BLUFFTON.EDU>]

I think it is amazing that the unit vector thread has produced the
divergent views it has, and also has produced some converts (me
included) who realized they might not have been viewing things 100%
correctly (or "positively pedantic" as Joel Rauber says).

Here is something pretty basic in our everyday teaching, and we do not
all view it the same.  That's amazing.  And it also is another example
of the wonderful value of e-mail and lists like this.

To answer Joel's most recent question about where we stash the units
when we write it, I use both methods.  I typically would write F =
(2N)i - (3N)j if I remember to do so.  However, it I get in a hurry and
write down F = 2i - 3j, and I realize: oops, I forgot the units, then I
can easily fix this (without erasing) by putting in parentheses and N
to yield F = (2i - 3j) N.  But that's not my preference.

One reason I do it only as an accident is because it somehow seems
wrong to associate the units with the complete vector (i.e. both the
magnitude and the direction).  I would ask this, if you routinely write
F = (2i - 3j) N, would you also write F = (3.61 at -56.3-degrees)
newtons?

I would not typically write that.  I would write F = 3.61 N at -56.3
degrees.


Michael D. Edmiston, Ph.D.              Phone/voice-mail:       419-358-3270
Professor of Chemistry & Physics        FAX:                    419-358-3323
Chairman, Science Department            E-Mail                  edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817



-----Original Message-----
From:   Joel Rauber [SMTP:Joel_Rauber@SDSTATE.EDU]
Sent:   Wednesday, September 22, 1999 8:50 AM
To:     PHYS-L@lists.nau.edu
Subject:        Re: Being careful with dimensions (was Re: i,j,k things)

Gang,

> > My problem with this is that I don't like the expression
> "F=2i-3j" that
> has
> > been used as an example throughout this thread.  In fact I
> hate it.  I
> > would always write "F = (2N)i - (3N)j".
> >
> > Am I in the minority???

The way I write it is "F = (2i - 3j) N"
Which of course begs the question;  unless you interpret my style as
meaning
the units go with the vector and the components or the unit vectors; (I
don't make such an interpretation, I have a more live-and-let-live
philosophy until I decide to get positively pedantic).  Any comments on
the
above style of writing the vector?
> Moreover, I think texts set a HORRENDOUSLY bad example when they
write
> things like, "The position of a ham sandwich is given by x =
> 3 - 5t + 2t^2,
> find its speed at t = 5 s."

I agree with John above, but am just as egregious as the texts, out of
laziness.  it gets awfully tedious to write:

x = 3m - 5 m/s t + 2 m/s^2 t^2

but I admit its laziness, and my students would probably be better
served if
I did it more properly; of course, there is a price, fewer examples
worked
in class.

> O.K., I know this probably qualifies as a pet peeve and that most pet
> peeves are at least borderline overreactions, but this one really
does
> push my buttons.

True too, but not all borderline overreactions are really
overreactions.

Joel Rauber