  Using an isospin- and momentum-dependent transport model we study effects of
the momentum-dependent symmetry potential on heavy-ion collisions induced by
neutron-rich nuclei. It is found that symmetry potentials with and without the
momentum-dependence but corresponding to the same density-dependent symmetry
energy $E_{sym}(\rho)$ lead to significantly different predictions on several
$E_{sym}(\rho)$-sensitive experimental observables especially for energetic
nucleons. The momentum- and density-dependence of the symmetry potential have
to be determined simultaneously in order to extract the $E_{sym}(\rho)$
accurately. The isospin asymmetry of midrapidity nucleons at high transverse
momenta is particularly sensitive to the momentum-dependence of the symmetry
potential. It is thus very useful for investigating accurately the equation of
state of dense neutron-rich matter.
