  In the present paper, we study the effect of the rotation on the masses of
scalar meson as well as vector meson in the framework of 2-flavor
Nambu--Jona-Lasinio model. The existence of rotation causes a tedious quark
propagator and corresponding polarization function. Applying the random phase
approximation, the meson mass is calculated numerically. It is found that the
behavior of scalar and pseudoscalar meson masses under the angular velocity
$\omega$ is similar to that at finite chemical potential, both rely on the
behavior of constituent quark mass and reflect the property related to the
chiral symmetry. However, masses of vector meson $\rho$ have more profound
relation with rotation. After tedious calculation, it turns out that at low
temperature and small chemical potenial, the mass for spin component $s_z=0,\pm
1$ of vector meson under rotation shows very simple mass splitting relation
$m_{\rho}^{s_z}(\omega)=m_\rho(\omega=0)-\omega s_z$, similar to the Zeeman
splitting of charged meson under magnetic fields. Especially it is noticed that
the mass of spin component $s_z=1$ vector meson $\rho$ decreases linearly with
$\omega$ and reaches zero at $\omega_c=m_\rho(\omega=0)$, this indicates the
system will develop $s_z=1$ vector meson condensation and the system will be
spontaneously spin polarized under rotation.
