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Re: [Phys-l] Symbols for Kinematics



On 08/09/2007 11:18 PM, Folkerts, Timothy J wrote:
.... This equation is commonly written as

v = v_0 + at

but there are many possible variations.

ARE THERE PEDAGOGICAL REASONS TO CHOOSE ONE OVER THE OTHERS?

What an interesting question. Actually in the last week we've
had three good discussions of some really basic physics.

I see three kinds of variations: In order from good to bad, we
have:
-- Starting from the definition of acceleration, even using
a single, consistent set of terminology, there are at least
half a dozen valid corollaries. Students should know them,
and know how one formula is related to the other formulas.

-- Even if consider only consistent sets of terminology, there
are many such sets. The choice of which set to use is partly
a matter of taste.

-- There are innumerable ways of making the terminology self-
inconsistent.

Here is my attempt to present the basic equations in a way that
is self-consistent, reasonably standard, and reasonably tasteful:
http://www.av8n.com/physics/intro-acceleration.htm

There is also some discussion of some notation I chose to avoid,
concerning the use of subscripts and the notation for functions.

There is also some discussion of which equations exhibit Galilean
invariance and time-shift invariance.

Comments and suggestions are welcome.

On 08/10/2007 12:10 AM, Dan Crowe wrote:
Arnold Arons argues that kinematic equations should be written in terms
of time intervals, not clock readings (instantaneous values of time).
See, for example, Arons, Arnold B. (1997)
_Teaching_Introductory_Physics_, Part I, pp. 23-25.

That is a quite a Jekyll-and-Hyde book. It contains a number of
good ideas, interspersed with quite a few bad ideas. Pages 23-25
are in the latter category. They define acceleration in a nonstandard
and obviously unsound way, and then spend several pages saying how
bad it is. Well, duh. It's like showing me a 40-cm-tall pile of
cactus and rusty nails, and then explaining in detail why I
shouldn't sit on it.

There ia a valid point to be made about writing fundamental laws
in manifestly invariant forms, but the point gets lost in all the
silliness ... and there are better ways of making the point.
http://www.av8n.com/physics/intro-acceleration.htm#sec-invariant