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Re: dimensionless units



I just had the following thought related to Michel's and David's comments


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.


It is probably not a good idea to leave out the names of units (whether
they are dimensioned or not) from the discussion when there are multiple
different common unit measures of how to measure the quantity in question.
Since the dimensionless quantity "angle" has multiple units: rad, deg,
grad, and cycle are all in extant use one ignores their names at one's
peril. This has nothing to do with angles being dimensionless. That is
a different issue.

I agree about leaving in the names of units. I wonder if it would help
students understand the idea that radians (or degrees for that matter) are
dimensionless units if you brought up the idea of measuring airplane speeds
in units of Mach numbers at the same time. My students are like Michaels in
that they are confused by this aspect of radian measure, but they seem to
understand Mach numbers quite well. So perhaps introducing the two ideas
simultaneously could be of some help.

My practice to date has been to mention mach number only in the context of
the last ten minutes of the lecture on Doppler shifts, when you ponder what
happens when the source speed is larger than the speed of the wave in the
medium.



Also, converting units is a *different* activity than doing dimensional
analysis.

*Very important statement that is not often appreciated by students*

All also would add in response to some other posts, there is nothing sacred
about three base mechanical dimensions. Relativists work all the time in
systems of units that only have two or one base dimension.

David Bowman
David_Bowman@georgetowncollege.edu


Joel Rauber
Joel_Rauber@sdstate.edu