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Re: dimensionless units



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.

For example, if the angular velocity (w) of a rotating disk is given as 6.28
radians per second, then you can calculate the frequency (f) of rotation by
w/2pi. But what shall we do with the units? It looks to students like the
frequency ought to be 1.00 radian per second. If we want it to be 1.00
reciprocal second (or 1.00 Hz), how do we "get rid of" the radians? I know
there are games we can play to do it... but it confuses the students.

I would rather say that the angular velocity is 6.28 reciprocal seconds and
the frequency is 1.00 reciprocal second (or Hz). That is, I just like to
leave the word "radian" completely out of the discussion.

Howdy,

It has become traditional to use "unitless" angles when referring to
radian measure ONLY. The problem with never using radian or degree
or rotation (yes, that is a [dimensionless] unit of angle too) is
that the number then has no meaning: 2 1/s could mean 2 rotations/s,
2 degrees/s or 2 radians/s which are very different. You must put in
the units (including rotation as a unit) to distinguish how many
there are when you go all the way around once
(1 rotation = 360 degrees = 2\pi radians).

By dimensionless I mean that the unit is not made of combinations of
the three fundamental units of measurement.

By the way, the number of atoms in an object is a dimensionless unit too.

Good Luck,
--
Herb Schulz
(herbs@interaccess.com)