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I claim that one can apply the 2nd law in a non-inertial frame
as long as one includes terms that represent what I call
"kinematical" forces. Others call them "fictitious" , others
"pseudo" others "apparent". In order to be neutral between
Marlow and me, I'll call them "apparent" for the time being.
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Note: the rhs of (2) is the total work done by all the forces and
includes work terms from the apparent forces. In fact, if there
are no "real"forces presents then this is work done solely
by apparent forces.
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in others words
Delta (kinetic energy)' = work done by real and apparent forces,
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Note: in order for this to be correct and consistent we must
include in the work terms of the apparent forces. i.e. those
terms produce measurable effects (effects measured in the
prime frame only!!). Namely, they contribute to the quantity
that is the lhs of (4).
Conclusion: applying the 2nd law as the equations of motion
in the non-inertial frame correctly produces the trajectory
of the object as measured in the non-inertial frame as long
as apparent forces are included in the sum of forces term.
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... I'll give a specific example, worked out in detail, of the work
produces the correct change in "kinetic" energy in a future post.
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Joel Rauber
rauberj@mg.sdstate.edu