  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 the light and strange quarks 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 complicated and
interesting. When extending to the situation with finite chemical potential, we
find the angular velocity also plays a crucial role, at small 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, it can
be observed that at very low temperature in the presence of quark chemical
potential the quark number susceptibility has two maxima with increasing
angular velocity. 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 also explored the phase diagram in the
$T$-$\omega$ plane, we observe that there exist first order phase transitions
for the rotating system and the first order phase transition lines move toward
a higher temperature for decreasing angular velocity. It is also found that the
different chemical potentials change the boundary of phase diagram, and that a
larger chemical potential shifts down the critical temperature. We expect these
studies to be used to understand the chiral symmetry breaking and restoration
as well as probe the QCD phase transition.
