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Re: little gee and its sign



At 01:23 PM 9/10/01 -0500, Tina Fanetti wrote:
The problem is over the sign of g, the gravitational acceleration.
...
I can't seem to explain to them why this is.
They tell me the book says it is positive.

Then at 04:50 PM 9/10/01 -0400, I wrote:

In the conventional coordinate system where the Z axis points vertically
upward, the z-component of the g vector will be a negative number -- but
this is not something of physical signficance; it depends on the arbitrary
choice of Z axis.
....
c) It is OK to say g dot Z is negative, for certain arbitrary
choices of Z.

To drive home the point: There are other perfectly reasonable coordinate
systems in which the Z-component of the vector g is positive. All you need
is a downward pointing Z-axis.

Example 1: In aerodynamics and aeronautical engineering, this is exactly
what you've got. The absolutely conventional airplane axes are shown in
this figure:
http://www.monmouth.com/~jsd/how/gif48/axes.gif

Example 2: In a problem where we drop an object from rest, the quantity
of interest is the distance it has travelled. Like all distances, this is
a positive number, and a student who writes
d = 1/2 g t^2
(where all quantities are positive) is committing no sin.

At 02:55 PM 9/10/01 -0500, Herb Schulz wrote:
I've
always taken points away from students that don't define the
coordinate system they are using in a given problem;

I agree that students should be taught to think clearly and communicate
clearly about their choice of coordinate system.

On the other hand, I think the foregoing overstates it a bit. Any
physically-significant calculation will give a final result that is
!independent! of the choice of coordinate system -- so if only the final
result is being presented, there is no reason why anything needs to be said
about the coordinate system.

In any case: Students should not be required to guess what coordinate
system the teacher would have used, nor penalized for choosing a different
one.