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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.

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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.

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  • $\begingroup$ 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 - $W_{conservative}+W_{non-conservative}+W_{external}=K_f-K_i$. $\endgroup$ – Guru Vishnu Nov 17 '19 at 7:32
  • $\begingroup$ @Intellex I would not provide a proof of the 1st equation as it would be a homework like proof but I would give you a hint that total work done by all forces is equal to change in kinetic energy which includes pseudo and coriolis forces as well.Remeber to calculate the work done by inertial forces from heliocentric reference frame.Is it fine now? $\endgroup$ – RunMachine_Kohli Nov 17 '19 at 8:03
  • $\begingroup$ Thanks. So we are proving this under the assumption "...total work done by all forces is equal to change in kinetic energy which includes pseudo and coriolis forces as well" which is same as saying the work energy theorem is valid in non inertial frames. Further, why "heliocentric reference"?, I'm not doing celestial mechanics. Even this frame is non-inertial. Am I right? $\endgroup$ – Guru Vishnu Nov 17 '19 at 8:18

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