Not all laws that hold in an inertial frame hold in a non-inertial frame. An obvious example is the law of inertia.
Does the Work-Energy Theorem necessarily hold in a non-inertial frame?
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Yes,work energy theorem is valid in non-inertial frames also.Only we've to take care of the pseudo forces & work done by them(fictitious work though).For example as in dynamics problems Newton's laws are applied after taking appropriate pseudo forces in non-inertial frames so do we apply work energy theorem & count work done by these pseudo forces & their effect on energy.