Since conservation of energy has come up a few times:
Suppose we break the KE down into components, just like the momentum.
KEx = Px^2/2m
KEy = Py^2/2m
KE = P^2/2m = Px^2/2m + Py^2/2m = KEx + KEy
so far this looks like it works - the components of kinetic energy in
the x and y directions add up to the total energy, as energy
conservation tells us to expect.
BUT - if KE is a vector, then its relation to KEx and KEy must be
KE = +/- SQRT(KEx^2 + KEy^2)
which can only match the equation above if KEx=0 or KEy=0, in which case
KE is a scalar not a vector
So, we do not have a consistent format for dealing with KE having vector
components.
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One more thing while I'm at it, if anybody does dig up references to KE
as a component of any vector this presents an opporunity to make sure
they understand the difference between a vector and its scalar
components.