Let's consider I have a particle moving on the x,y plane. On this particle acts the Lorentz force, however it does not necessary perform a rotation by the axes origin . I would like to re-write the Lorentz force in the "global" cylindrical coordinate system where the origin is the same as the r=0. Of course the particle motion will be described by and in that coordinate system. Should I add an inertial force in this system, such as , in my description?