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Re: Problem



On Wed, 19 Sep 2001, Michael Edmiston wrote:

I am using Tipler and I looked at page 126 like Joel suggested. In this
example Tipler gives a specific name (tangential acceleration) to the
concept, and he does not use absolute value notation when he writes a(tang)
= dv/dt.

I don't have Tipler in front of me but I assume that the "v" you
refer to is not in boldface and does not have a vector symbol
above it, that is, that it represents the usual shorthand
notation for |v|, the magnitude of the vector velocity.

So I am partly asking about the d|v|/dt notation, and I am partly asking
what we call this. Would the name "tangential acceleration" be correct in
general? If we are dealing with 2-D or 3-D motion, my first impression
would be dv/dt implies d|v|/dt if the v is not bold or does not have an
arrow; and it seems the name "tangential acceleration" would be an
appropriate name in general.

Yes. I would (and do) call it tangential acceleration. It *is*
the component of the acceleration "tangent" to the trajectory with
the plus sign assigned to the direction of the instantaneous
velocity.

Perhaps the more problematic question is what to call the
component that is locally perpendicular to the trajectory. I,
personally have no problem with calling it centripetal
acceleration (where we would understand that it is the component
toward the instantaneous center of curvature of the path and is
given by v^2/R where R is the distance to the instantaneous center
of curvature), but I know that some people prefer to use the
phrase "centripetal acceleration" only when the trajectory really
*is* (at least for a while) a circle.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm