The equations of state for neutron matter, strange and non-strange hadronic matter in a chiral SU(3) quark mean field model are applied in the study of slowly rotating neutron stars and hadronic stars. The radius, mass, moment of inertia, and other physical quantities are carefully examined. The effect of nucleon crust for the strange hadronic star is exhibited. Our results show the rotation can increase the maximum mass of compact stars significantly. For big enough mass of pulsar which can not be explained as strange hadronic star, the theoretical approaches to increase the maximum mass are addressed.
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