Figure 2 shows the "centrifugal term" r θ θ ˙ ˙ 2 does not transform as a true force. Suppose in frame S a particle moves radially away from the origin at a constant velocity. See Figure 2. The force on the particle is zero by Newton's first law. Now we look at the same thing from frame S' , which is the same, but displaced in origin. In S' the particle still is in straight line motion at constant speed, so again the force is zero.