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Re: Problem



Thanks to Joel and John for trying to answer my question, but
I am still not
sure if it has been answered. I understand the words you are
saying, but I
am asking if the notation and nomenclature is anything anyone
has agreed
upon.

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 have seen two names for this:

1) tangential acceleration (as the tangential component of a_vec is parallel
to the Velocity vector which is tangential as well) Tangential to what? The
path of motion.

2) Parallel component.

Similarly I've seen two names for the other component

1) Centripetal acceleration
2) perpendicular component


IMO either nomenclature is true in general and extends to all integer
dimensions. And is fairly common.

I prefer the absolute value bars as it makes it clear that the derivative is
a derivative of a scalar (magnitude of v_vec) and not the derivative of a
vector.




*(The following is for the masochists)*:


If I were to be very pedantic I'd say (in 3D case).

a_perp (underscore means previous quantity is vector

a_parallel = a_tan = d|v_|/dt * (v_/|v_|)

where d|v|/dt = d/dt (Sqrt(vx^2 + vy^2 + vz^2))

and


a_perp = |v_|/r^2 * unit vector

The unit vector points perpendicular to v_ and lies in the instantaneous
plane of the trajectory of the particle and points to the interior of the
curve, and r is the radius of curvature of trajectory at the point in
question.

more succinctly

unit vector = d/dt ( v_/|v_|) / |d/dt(v_/|v_|)|, no proof provided.

To say more, or to extend into higher dimensions takes me farther into the
realm of differential geometry than I remember or care to go at the moment.

Hopefully, typos in the above have been minimized.