A fictitious force, also known as a phantom force, pseudo force, d''''Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, like as a rotating reference frame.
The force F does not arise from any physical interaction but rather from the acceleration a of the non-inertial reference frame itself. As stated by Iro: like an additional force due to nonuniform relative motion of two reference frames is known as a pseudo-force.
— H Iro in A Modern Approach to Classical Mechanics p. 180
According to Newton''''s second law in the form F = ma, fictitious forces always are proportional to the acceleration a.
A fictitious force arises when a frame of reference is accelerating compared to a non-accelerating frame. As a frame can accelerate in any arbitrary way, so can fictitious forces be as arbitrary (but only in direct response to the acceleration of the frame). Though, four fictitious forces are defined for frames accelerated in commonly occurring ways: one caused by any relative acceleration of the origin in a straight line (rectilinear acceleration), two caused by any rotation (centrifugal force and Coriolis force) and a fourth, known as the Euler force, caused by a variable rate of rotation, should that happen.