Work associated with pseudo force In a non inertial frame if I want to apply the Newton's laws of motion one would use the help of pseudo force but in non inertial frame if I try to apply the work energy theorem should I consider the work done by the pseudo force or not?
I mean because pseudo force does not exist i.e. it is virtual force, so does it have any real work or its work is not to be considered?
 A: Pseudo-forces in the non-inertial frame cause an apparent change in for instance kinetic energy. And thus, they do apparent work, or "pseudo-work", if you will.
For example, consider standing on roller-skates in a driving bus. In the non-inertial frame of the bus, when the bus brakes you roll forward, as if a pseudo-force is pushing you and accelerating you to speed up and reach higher kinetic energy.
In reality, it is not you who are gaining kinetic energy, but rather the bus that is losing kinetic energy. But in the frame of the bus, it does appear to be you who gain apparent kinetic energy. This must be due to some apparent "pseudo"-work done by the apparent pseudo-force.
Basically, in non-inertial frames, pseudo-forces act and function just like any other force. They can do work etc. just like any other. Their work just is also "pseudo".
A: Pseudo forces are introduced in non-inertial frames in order to save
Newton's second law. Work-energy theorem is a direct consequence of
second law, so if second law holds energy-theorem also applies.
A: Consider an object with no force acting on it in a non inertial frame, e.g. a frame in rotation with respect to CMB. If you don't take inertial pseudo-forces into account, it means that no force will work on the object in this frame, hence it must have a rectilinear uniform movement in strictly any frame you can think of. For example, it would be still with respect to the CMB AND to this rotating frame (or with a constant velocity).
This is obviously not possible. As a matter of fact, no local experiment will tell you at a specific moment if you are in a non galilean frame or if there exists a gravitational field acting. But in newtonian physics, you take gravity into account when you list the "forces" working on your object. So the same must be true for any inertial "force".
