  Properties and structure of neutron stars are determined by the equation of
state (EOS) of neutron-rich stellar matter. While the collective flow and
particle production in relativistic heavy-ion collisions have constrained
tightly the EOS of symmetric nuclear matter up to about five times the normal
nuclear matter density, the more recent experimental data on isospin-diffusion
and isoscaling in heavy-ion collisions at intermediate energies have
constrained considerably the density dependence of the nuclear symmetry energy
at subsaturation densities. Although there are still many uncertainties and
challenges to pin down completely the EOS of neutron-rich nuclear matter, the
heavy-ion reaction experiments in terrestrial laboratories have limited the EOS
of neutron-rich nuclear matter in a range much narrower than that spanned by
various EOSs currently used in astrophysical studies in the literature. These
nuclear physics constraints could thus provide more reliable information about
properties of neutron stars. Within well established formalisms using the
nuclear constrained EOSs we study the momenta of inertia of neutron stars. We
put the special emphasis on the component A of the extremely relativistic
double neutron star system PSR J0737-3039. Its moment of inertia is found to be
between 1.30 and 1.63 $(\times10^{45}g$ $cm^2)$. Moreover, the transition
density at the crust-core boundary is shown to be in the narrow range of
$\rho_t=[0.091-0.093](fm^{-3})$.
