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RE: supplementary S.I. units

Is not the radian defined as a ratio of arc length to radius, and as such
all
unit cancel !!??
Oren Quist, SDSU

----------
From: Joe Baughman
Sent: Tuesday, September 22, 1998 12:40 PM
To: phys-l
Subject: Re: supplementary S.I. units


At 10:37 AM 9/22/98 -0600, you wrote:
I was intrigued by a note in this month's (September) issue of AJP (vol.
66, No. 9, page 814) which referred to a previous article from July last
year (AJP, vol. 65, No. 7, pages 605-614) about making radians a real
(base
S.I.) unit rather than a supplementary unit. I would like reaction from
you brilliant people about the whole idea (I'm quite attracted to the
notion that "radain units need never be spuriously inserted or
deleted"),
but also in particular to the comment in the note that "we usually
forget
that areas and length squared, or volumes and length cubed, are not the
same thing." I thought that was the whole reason we use meter cubed for
the S.I. unit of volume instead of the liter.



Perhaps the distinction between area expressed in square units (ie,
inches
squared) and "length squared" is because in math, I can find area or I
can
take a single length and square it for some reason.

I envision that area would be a subset of any unit squared. In other
words
meters squared would be the set and it could express a "length squared"
or
an expression of an "area".

My students get confused somethimes when they encounter the expressions
"square meters" (an area perhaps) and "meters squared" (a length that is
squared, perhaps). It is a distinction I have never really gotten into
in
class.

I too wonderously have Radians appear in a problem answer that appears to
be
dimensionless. I also am intrigued by the idea of using radians as a
base
unit. Maybe use of this "base" unit will clear up some confusions that
arise that rotational distance can be expressed in radians, revolutions,
degrees, gradients, etc., but when you work out calculations one must
usually express the unit in terms of radians.

--------------------------------------------------------------------------
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Joe Baughman e-mail:
joebau@blueridge.cc.nc.us
Science & Mathematics Instructor
Blue Ridge Community College Telephone: (704)692-3572 x301
College Drive Fax: (704)692-2441
Flat Rock, NC 28731-9624

Web Server: http://www.blueridge.cc.nc.us/
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