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-----Original Message-----/SNIP/
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Tuesday, August 14, 2007 8:21 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Motion in 1D, vectors and vector components
One common cause of confusion in kinematics problems in general,I think it would be beneficial to physics learners in general if we
affecting students from high school to grad school inclusive, has
to do with drawing physical vectors versus drawing basis vectors.
In one dimension, suppose the basis vector points to the right,
and suppose the physical vector points to the left. The physical
vector can be drawn to scale (including magnitude as well as
direction) as an arrow pointing to the left. The physical vector
can be represented numerically as a negative number times the basis
vector.
This does *NOT* mean that you have a negative amount of the leftward
arrow! That would be double-counting the minus sign (and squaring
the magnitude as well). The leftward arrow is complete unto itself.
Constructive suggestion: Always label your vectors so as to make
it clear what is a basis vector and what is not.
True story: This was one of my first experiences in graduate
school: The very first homework assignment involved a vector
pointing to the left. Every first-year student diagrammed it
as an arrow pointing to the left, and quantified it as a negative
number. The grader (a third-year grad student) marked every
student wrong.
We got out our torches and pitchforks and marched to the grader's
office:
http://mag.awn.com/issue9.02/9.02images/wolff09_VanHelsing-
villager.jpg