We investigate the rotating quark matter in the three-flavor Nambu and Jona-Lasinio (NJL) model. The chiral condensation, spin polarization and number susceptibility of strange quark are carefully studied at finite temperature without or with finite chemical potential in this model. We find that the rotation suppresses the chiral condensation and enhances the first-order quark spin polarization, however for the second-order quark spin polarization and quark number susceptibility the effect is very interesting, in the case of zero chemical potential which have a jump structure when the first-order phase transitions take place. When extending to the situation with finite chemical potential, we find the angular velocity also plays a crucial role, at small or large enough angular velocity the chemical potential enhances the susceptibility, however in the middle region of angular velocity the effect of the chemical potential is suppressed by the angular velocity and susceptibility can be changed considerably, which can be also observed that the quark number susceptibility has two maximum value. Furthermore, it is found that at sufficiently large angular velocity the contributions played by light quark and strange quark to these phenomena are almost equal. We expect these studies to be used to understand the chiral symmetry breaking and restoration as well as probe the QCD phase transition.
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