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Re: [Phys-l] backwards units : entrenched usage




The other day I was reading the data plate on an electric motor:

HP : 1 1/3 Type : C
RPM : 1725 SF : 1.0
A : 12.3 PH : 1
V : 115 Hz : 60

This seems backwards relative to the way we would write things in the
physics lab:

1.333 HP
1725 RPM
12.3 A
115 V
60 Hz

The problem of backwards units is firmly embedded in math as taught in the
US. It goes much deeper in that units are used as variables, and math does
not distinguish between them. So if you pose the following question "The
number of apples in the box is 15. What is the variable" Students will
reply "apples", but "number" is the variable. So this problem begins in
elementary school and is reinforced there.

Then when students do math they are told that a ball is dropped from a
bridge and accelerates downward. The formula for the distance traveled in
meters is y=4.9x when x is measured in seconds. How far has the ball
traveled after 2 seconds. But often the problem is expressed without any
reference to units. Notice how the problem associates the units with the
variables rather than with the constant. So the problem is reinforced in HS
math.

The deep embedding of backwards units is just a symptom of the way that
units and variables are not distinguished in math. It is not a problem if
you understand what is going on. We all use shorthand or idioms which can
be deceiving. So the question "How many grams are in the sample" is just as
good as "What is the mass of the sample in g", but the second one should be
used in texts and by teachers. Math teachers should be aware that students
are not picking up the idea of variable very well.

John M. Clement
Houston, TX