General geodesic equations of the motion of spinning systems around the (31)-dimensional and (2+1)dimensional rotating anti-de Sitter black holes an
obtained. Based upon these equations, we derive the entropy bound for a rot
ating system from Kerr-anti-de Sitter black holes and Banados-Teitelboim-Za
nelli black holes, respectively. Our result coincides with that of Hod's de
rived from a Kerr black hole, which shows that the entropy bound of the rot
ating system is neither dependent on the black hole parameters nor on space
time dimensions. it is a universal entropy bound.