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