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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.