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Re: dimensionless units



On Wed, 29 Nov 2000, David Bowman wrote:

Regarding Michael's comments:

I don't totally disagree with Denker and others who want to say that
"radians" are units, but dimensionless units, but it sure causes problems
for students who are trying to do dimensional analysis.

Not if they are careful.
[...]

Also, converting units is a *different* activity than doing dimensional
analysis. Dimensional analysis mostly involves power counting of a set
of base dimensions. When doing dimensional analysis *none* of the
dimensionless quantities contribute to the dimension of the result of a
product or quotient of mutliple qunatities *no matter* which units any
dimensionless quantity is measured in. But when converting units (or

We all have this clear, but many times this is not so for students.
I agree with Michael's comment. For instance, when studying the transient
effects in a RL circuit, its not necessary to memorize how '\tau' is
given in terms of the parameters and magnitudes involved in the problem.
As the product Lw has the dimensions of a resistance, \tau must be
given by (Lw/R) times a time. I've seen students looking around for
a magnitude with dimensions of a time without finding it, just
because for them [w] = rad/s, and they couldn't get rid of those
radians...Another examples is when relating w and the frequency f
of a sinusoidal signal...

Well, this may probably be extreme cases.

Regards,
Miguel A. Santos