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Re: dimensionless units



On Thu, 30 Nov 2000, Robert A Cohen wrote:

Shouldn't we treat the radian the same way? Isn't the radian equivalent
to (m of arc)/(m of radius)? [note that any unit of length could be used]

In fact, this is precisely the point that underlies the "elaborate
and absurdly pedantic" method that "I like very much" and to which
I referred in my previous posting. In that method, we define all
angular quantities in terms of a parameter called r' which is the
"tangential distance per unit angle." Thus, angles are given by

theta = s/r'

where s is the asociated tangential distance.

For example, to find the angle associated with a tangential
distance of 10 cm at a distance of 50 cm from the apex, one
"simply" uses

s = 10 cm

and

r' = 50 cm/rad = 0.873 cm/degree = 314 cm/cycle = 0.785 cm/grad

It gets for more interesting than this (in my view) and
establishes a consistent approach to the treatment of "angular
dimension", but I won't belabor the point here. If you want to
read more, go to the archives

http://mailgate.nau.edu/archives/phys-l.html

and search for

Units and dimensions in rotational dynamics

to find my 12 September 1996 posting.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm