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Re: [Phys-l] frequency: a modest proposal



There's no problem with work and torque. Torque has (SI) units of J/rad
so that if you the points on a body to which you are applying a constant
torque rotate through an angle theta measured in radians, in the same
sense with respect to the same axis as for the torque, then you have
done an amount of work equal to the product of the torque in J/rad and
the anglular displacement in rad.

One interesting aspect of the proposal that we be more consisitent in
the way we deal with units is that the r in the equation
s = r theta
relating arc length on a circle to angle subtended would have units of
length per angle, e.g. meters/radian. It would no longer be the same
thing as the distance from the center of the circle to a point on the
circle--that quantity would have units of length, e.g. meters. As with
most equations, you could use any dimensionally consistent units for r,
e.g. m per degree or feet per rotation but the value would only have
the same pure number part as that of the distance from the center of a
circle to the point on the circle if the units are units of length per
radian (and the units of length in this quotient are the same ones as
used for the distance from the center to a point on the circle). (I
read about a proposal to define the r in s = r theta as described here.
It is not original with me. Sorry I don't recall where I saw it.)

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Clement
Sent: Tuesday, February 02, 2010 3:10 PM
To: 'Forum for Physics Educators'
Subject: Re: [Phys-l] frequency: a modest proposal


On 02/02/2010 07:45 AM, Edmiston, Mike wrote:
John Denker suggested saying "cycles per second" rather than "per
second" if frequency is what we are talking about. I would
presume
we would also say "radians per second" rather than "per second" if
angular frequency is what we are talking about.

Agreed. (The only reason I emphasized the Hz example
is that it is where this thread started, and it is
the problem child on the NIST web page. It is not
a particularly special case.)


Of course one should actually go whole hog. So wavelength would be
m/wave
or m/cycle. If one actually explicitly puts in these objects, then
when you
get the end result things should cancel or the necessary conversions
should
be obvious. So if you get cycle/radian you know what to do.

The view of units as just telling you the dimensions may be a bit
narrow.
So one could include all objects rather than just commonly spatial,
mass,
and time dimensions.

This might help students quite a lot by typing all numbers to
appropriate
units. So if you are given 2m as a measurement why not be much more
specific and say 2m/person-height so now you know exactly what it
means.
Then of course the next advance would be to have calculators and
programs
that handle units of this sort so they could do some modest checking
for
you. Of course there is always the distinction between work and
torque, but
I suspect a suitable notation could be worked out.

John M. Clement
Houston, TX

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