Re: speed and velocity

[Bob Sciamanda <trebor@VELOCITY.NET>]

This is a good idea - I introduce "negative" components in just this way,
but then put the sign out front, to get to usual practice.
Our computational apparatus does things like A_x = Acos(X) , where X is
the angle between the directions of A and the unit vector x^.  Thus all
of our computational machinery spits out a sign with each vector
component.
 IOW, each component of a 3-vector is a 1-vector which carries a sign for
direction (the sign is a unit vector in the one dimensional sub-space).

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor
-----Original Message-----
From: Tim Folkerts <tfolkert@BIGCAT.FHSU.EDU>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Wednesday, November 25, 1998 12:57 PM
Subject: Re: speed and velocity


> I just had a thought (which probably isn't original and it is evolving
as I write this) but how about
> putting the sign with the unit vector rather than the coefficient out
front.  So a motion in the -x
> direction with a speed of 2 m/s would be
>        v = (2 m/s)(-i^)
>
> This emphasizes the vector nature AND the magnitude being a positive
quantity.  The coefficient is
> always positive and carries the units, while the vector nature is
wrapped up into a dimensionless,
> unit length vector.
>
> A speed of 2 m/s 45 degrees below the x axis could be either
>        v = (1.414 m/s)(i^) + (1.414 m/s)(-j^)
>    or
>        v = (2 m/s)(0.707 i^ - 0.707 j^)
> The first form is easier for addition; the second emphasizes the speed.
>
> In general then, any vector would be written in "standard form" as A =
(|A|)(A^), which matches
> exactly the mantra of "a vector is a quantity with a magnitude and a
direction".  The "quantity"
> contains the magnitude and units, while the "direction" is always given
by a unit vector, which you
> can either leave as A^ or convert to (cos(theta) i^ + sin(theta) j^ ).
>
> I would advocate always putting in the parentheses to emphasize the two
"parts" of a vector.  In
> fact, other than this emphasis, it's of course no different than
standard polar or cartesian
> coordinates.
>
>
> Comments???
>
>
>
> Tim Folkerts