Date: Sun, 8 Jun 1997 22:58:48 -0400
From: Alexander Bogomolny
Stephanie:
> Hi! I don't know if this question is a fit for your page or not:
Hi! I do not know if this answer is what you expected. Anyway.
Encyclopaedia Britannica has an article on Dimensional Analysis. You may get it on-line if you have access to the on-line edition.
In essence, some quantities depend on units of measurement (and are said to have a dimension or to be dimensional), other quantities do not depend on units ( and are said to be dimensionless or pure.)
Counting produces pure numbers, weighing does not. The numerical expression of weight of the same body depends on whether one uses pounds or killograms.
In dimensional analysis each line of mutually convertible units (like pound, killogram, ounce, etc.) is assigned a symbol. For example:
T is time M is mass L is length O is radian (actually, dimensionless) etc.
Derivatives of these are
LT-1 for speed LT-2 for acceleration LT-2M for force
Whether the theory is widely used outside the classroom I can't say. In principle, physical laws may be discovered using dimensional analysis - probably none was. But whenever you do some calculations the theory might be useful (in classroom or outside.) I am sure I have used it several times on random occasions.
Now, the theory just says that you can't add apples and oranges. Whatever you add must be of the same dimension. So, if after calculations you get a formula whose dimension is LT + L/T, you should retrace your steps and fix an error. If you are looking for radians but the result has dimension L or 1/L, the result simply can't be correct.
For me, dimensional analysis is an easy safeguard against avoidable errors.
Sincerely,
Alexander Bogomolny
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