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.

While applying above theorem in centre of mass frame(non-inertial or accelerated) will not  necessisate even this.

yes, we can apply work energy theorm in non inertial frame provided we take into account the work done by the pseudo force also.

Take for simplicity a non inertial frame which has only transational acceleration 'α' .In this frame 2nd law will take the form

m*dv/dt = F - mα ,,,...now allpying the work energy theorm, we gat

0.5*m*(V_{²f - V²i )} = int(F.dr) - m *int(α.dr )

Thus in case of a non inertial force kinetic energy not only changes due to work done by material forces but also due to pseudo forces.....

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