  General geodesic equations of the motion of spinning systems around the
(3+1)-dimensional and (2+1)-dimensional rotating anti-de Sitter black holes
have been obtained. Based upon these equations, we derived the entropy bound
for a rotating system from Kerr-Anti de Sitter black holes and BTZ black holes,
respectively. Our result coincides with that of Hod's derived from Kerr black
hole, which shows that the entropy bound of the rotating system is neither
dependent on the black hole parameters, nor on spacetime dimensions. It is a
universal entropy bound.
