惯性坐标系

In linear motion, it is possible to do something called a Galilean transform. A Galilean transform lets us change all positions (e.g., replace $x$ with $x+x_0$ everywhere) or velocities (e.g., replace $v_x$ with $v_x + v_{x,0}$ everywhere). Under this transform, we find that the acceleration and forces are the same, and the motion of objects is the same (after changing positions and velocities). This is closely related to special relativity, which claims that there is no special frame of reference in which we should use to do these calculations.

The same is not true for rotational motion. While it is true that we can add a constant angle to everything, e.g. $\theta \to \theta + \theta_0$, we cannot choose an arbitrary rate of rotation. As seen from the fictious forces, a rotating system seems as if it has extra forces. Nature has a preferred frame of reference, called the inertial frame, in which it makes sense to say that the rotation rate is "zero". The Foucault pendulum experiment shows that standing on the Earth is not that frame of reference, since the Earth is rotating.