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*From*: John Denker <jsd@av8n.com>*Date*: Tue, 19 Jan 2010 05:43:23 -0700

On 01/18/2010 02:16 PM, Jeff Loats wrote:

On the first day of class I do a brief example to illustrate unit conversion

(snore) and I usually spice it up ....

On a completely serious note, here are some points

that you might want to think about in connection with

units. There is a fairly natural segue from units

to dimensions, and from dimensions to scaling.

1) Units are *not* the same as dimensions. The

existence of dimensionless units such as "degrees

of arc" should suffice to prove this point.

http://www.av8n.com/physics/dimensionless-units.htm

Units and dimensions are not entirely the same,

but they're not entirely unrelated, either. If

you know the units you know the dimensions (but

not conversely).

A lot of students have misconceptions about this.

2) Sometimes dimensional analysis is presented as

if it were a law of nature ... which it is not.

Dimensional analysis should be considered a

heuristic for guessing the scaling behavior.

Like all heuristics,

-- In skilled hands, it is a way of getting

the right answer quickly.

-- In unskilled hands, it is a way of getting

the wrong answer quickly.

===========

I mention this because scaling laws are tremendously

important. Given any discussion of units, I would

be unable to resist the temptation to segue from

units to dimensions, and then from dimensions to

scaling.

Scaling laws have been central to physics since

Day One of the modern era (1638) and remain so even

now. IMHO, they are grievously underemphasized in

the typical curriculum. They are IMHO more useful

*and* easier and more age-appropriate than most of

the stuff that is in the curriculum.

For more on all this, see

http://www.av8n.com/physics/dimensional-analysis.htm

and especially

http://www.av8n.com/physics/scaling.htm

**Follow-Ups**:**Re: [Phys-l] units, dimensions, scaling***From:*ludwik kowalski <kowalskil@mail.montclair.edu>

**Re: [Phys-l] units, dimensions, scaling***From:*"Jeffrey Schnick" <JSchnick@Anselm.Edu>

**References**:**[Phys-l] Fun/cool unit conversion example?***From:*Jeff Loats <jeff.loats@gmail.com>

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