In rotating frames, particles do not travel at constant velocity? If we measure a particle's trajectory in a rotating frame of reference as $\vec x=\vec x(t)$, then $\frac{d^2\vec x}{dt^2}=0$ could be zero? 
I'm trying to explain why the Newton's first law of motion is only true for a special frame of reference.
 A: 
If we measure a particle's trajectory in a rotating frame of reference as $\vec x=\vec x(t)$, then $\frac{d^2\vec x}{dt^2}=0$ could be zero? 

Of course. Consider a geostationary communications satellite. Ignoring perturbations, a geosynchronous satellite is stationary from the perspective of an observer fixed with respect to the rotating Earth. From this perspective, a geostationary satellite has zero velocity, so obviously, zero acceleration.

I'm trying to explain why the Newton's first law of motion is only true for a special frame of reference.

The contrapositive to Newton's first law is that a body subject to a non-zero net force will not be move with a constant velocity. Yet that geostationary satellite is moving with a constant velocity (zero) even though a force (gravitation) acts on the satellite. This is not consistent with Newton's first law.
That geostationary satellite is not stationary from the perspective of an inertial frame of reference. This is consistent with the first law of motion. A force is acting on it, gravitation.
