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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.
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.