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Re: speed and velocity



Hi Bob,
You are probably right in judging our main difference to be semantic.

I would make a real distinction between component vectors, which is what you
refer to in (1) and the components of a vector , which is what I referred to
in my previous e-mail. The former are vectors; the latter (often called the
x and y components) are not.

My worry is that there is a seat of confusion for students in all this, even
if - no, especially if - we gloss it over.

I quite like the presentation on pages 54 -62 of the preliminary edition of
Randall Knight's new IUPP text (Physics, A Contemporary Perspective, Addison
Wesley).

Brian McInnes

----------
From: Bob Sciamanda <trebor@VELOCITY.NET>
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: speed and velocity
Date: Thu, 26 Nov 1998 7:30 PM


Hi Brian,
I don't think we have a conceptual argument - only a language difference.
But in that vein, I would respond:
1) Since a vector is the sum of its components, those components must
also be vectors (apples and oranges).
2) I would accept calling the sign of a 1-d vector a "direction
indicator" instead of a subspace unit vector.

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: Brian McInnes <bmcinnes@PNC.COM.AU>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Thursday, November 26, 1998 1:54 AM
Subject: Re: speed and velocity


Bob Sciamanda sent three interesting e-mails to the list earlier today.

I have a problem with his definition of a one-dimensional vector as a
component of a three-dimensional vector, carrying a sign for direction.

As I understand it a component is obtained by a vector dot product and
is a
scalar, not a vector. the sign is not the direction of a vector but a
consequence of whether the angle involved in obtaining the component is
less
or greater than pi/2. In particular, vectors do not have signs, they
have
directions; they are intrinsically positive.
What we can do (and this was the line that Tim Folkerts took as along)
is to
associate the components with a unit vector along the special
one-dimension
line.

I agree that "mathematical models are our own constructs, subject to our
own
definition and use" but
it's preferable if we have common definitions and use.

Brian McInnes