vB, plus two extra terms related to the rate of change of the frame-B coordinate axes. One of these is simply the velocity of the moving origin vAB. The other is a contribution to velocity due to the fact that different locations in the non-inertial frame have different apparent velocities due to the rotation of the frame; a point seen from a rotating frame has a rotational component of velocity that is greater the further the point is from the origin. To find the acceleration, another time differentiation provides: Using the same formula already used for the time derivative of xB, the velocity derivative on the right is: Consequently, The interpretation of this equation is as follows: the acceleration of the particle in frame A consists of what observers in frame B call the particle acceleration aB, but in addition, there are three acceleration terms related to the movement of the frame-B coordinate axes: one term related to the acceleration of the origin of frame B, namely aAB, and two terms related to the rotation of frame B. Consequently, observers in B will see the particle motion as possessing "extra" acceleration, which they will attribute to "forces" acting on the particle, but which observers in A say are "fictitious" forces arising simply because observers in B do not recognize the non-inertial nature of frame B. The factor of two in the Coriolis force arises from two equal contributions: (i) the apparent change of an inertially constant velocity with time because rotation makes the direction of the velocity seem to change (a dvB/dt term) and (ii) an apparent change in the velocity of an object when its position changes, putting it nearer to or further from the axis of rotation (the change in due to change in x j ). To put matters in terms of forces, the accelerations are multiplied by the particle mass: The force observed in frame B, FB = maB is related to the actual force on the particle, FA, by where: Thus, problems may be solved in frame B by assuming that Newton's second law holds (with respect to quantities in that frame) and treating Ffictitious as an additional force. Below are a number of examples applying this result for fictitious forces. More examples can be found in the article on centrifugal force. Rotating coordinate systems A common situation in which noninertial reference frames are useful