# Is work-energy theorem valid in non-inertial frames?

From this answer for the question Is the energy conserved in a moving frame of reference?, I learnt that the work-energy theorem is independent of the frame of reference. But, is the theorem valid even for non inertial frames? I know that in non inertial frames we need to include inertial (pseudo or fictional) forces. Is the work done by all forces including the inertial forces equal to the change in kinetic energy?

Please note: According to this question and answer - Work associated with pseudo force, the work done by pseudo forces must be included in order to determine the total work done by all the forces. But the answer doesn't discuss about the validity of the theorem itself.

Yes why not, work energy theorem for a system of particles accelerating w.r.t an inertial frame is given as:-For an $$n$$ particle system let the inertial force on $$i^{th}$$ particle be$$\vec{F_{inertial}}^i$$ then,$$\sum_{i=0}^n \int (\vec{F_{inertial}}^i+\vec{F_{pseudo}}).d\vec{s}=\Delta K_{system}$$ $$W_{inertial}+W_{pseudo}=\Delta K_{system}$$ wheres change in mechanical energy of the system is given as $$\Delta E_{mechanical}=W_{ext}+W_{int,non cons}+W_{pseudo}$$ $$W_{int,non cons}$$ is the work done by internal non conservative forces of the system.
• With respect to your first equation, I think inertial and pseudo forces are the same. Further, from where did you get the first equation of work-energy theorem? Till now, I've only encountered only this form - $W_{conservative}+W_{non-conservative}+W_{external}=K_f-K_i$. – Guru Vishnu Nov 17 '19 at 7:32