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Re: vector directions



I agree with Joel. Only when measuring angular displacement in
rotations is it necessary to consistently measure angles in the
same direction from the same reference direction, and even then
it isn't necessary to always measure angles CCW from the
positive x-axis.

Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org

(Note: I resent this message because I forgot to keep each line
short the first time I sent it.)

-----Original Message-----
From: RAUBER, JOEL [mailto:JOEL_RAUBER@SDSTATE.EDU]
Sent: Friday, October 03, 2003 9:39 AM
To: PHYS-L@lists.nau.edu
Subject: Re: vector directions


Mike E. wrote in part:

. . .
Part of the problem stems from the fact that students tend to view the
trig relationships from a right triangle perspective. If the
vector is
-3i + 4j they are going to draw a right triangle in quadrant II and
solve for the angle of that triangle. Some of them won't
even get that
correct... they'll invert the 4/3 and find the arctan of 3/4.
Some will
include the minus sign and some won't. So we might get any of the
following answers... ( 53.1, -53.1, 36.9, -36.9 )... when the correct
answer is 126.9 degrees.


. . .

The correct answer is 126.9 degrees only if you have defined the correct
answer to be the angle measured CCW from the positive x-axis.

Perhaps in a high school class that is fine.

However, I tell my students I'll accept any of the angles mentioned above if
they tell me unambigously how they are measuring the angles (relative to
what and what they are calling positive vs. negative angles) and if their
answer matches their fiducial statements.

If they don't tell me I tell them I'll grade according positive angles being
measured CCW from the positive x-axis.

Joel R