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Re: Zero with units?



??? Suppose I am trying to have a student find the displacement of an
object that has an initial position of "0" and a final position at 5
meters. The student would then be expected to subtract the dimensionless
position "0" from the dimensioned quantity of 5m. This is quite contrary to
the approach that most of us try to instill in the students, where only
terms of similar dimensions can be added or subtracted.

Am I simply misunderstanding the point?

Bob at PC

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On 9/16/2004 at 3:06 PM Hugh Haskell wrote:

That was me. I agree that the Celsius and Farenheit temperature
scales are a special case, since their zero points represent
different points on the underlying absolute scales. But Kelvin or
Rankine scales don't have that problem, since their zero points are
at the same location.

But temperature is the only dimension I can think of that has this
property. If I am giving the temperature of something in, for example
Celsius, and the result comes out to be zero, then I do need to
specify the units, since an object at 0 degrees Celsius is at a
different absolute temperature than something at 0 degrees Farenheit.
But if I am interested only in temperature *differences* then the
problem goes away, since a temperature difference of zero is still
zero regardless of the temperature scale I am using (except, of
course, for the effects of ever more precise measurements, which may
show the actual difference to be other than zero, but that is another
issue).

Every other unit that I can think of, has the property that they are
not established compared to an absolute reference, so all one is
really measuring is differences. If to points are on the same circle
centered at an arbitrary origin, then their difference in distance
from that origin is zero in any distance units you might choose. The
same is going to be true of any other property one may measure. So
technically, units associated with a zero difference are unnecessary,

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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