The motions of dust particles in a strongly coupled quasi-2D dusty plasma system are studied using direct optical monitoring. After the short-time antipersistent caged stage, the series excitation and relaxation of rotational motions follow the random phase stick-slip rule for the harder melting state but are the non-stick-slip type for the softer liquid state. The former leads to the persistent and then normal diffusion, and the latter to the almost normal diffusion. Their effects on the spatial correlation of particle displacement are also studied.
