Phonon-dispersion curves along the threefold axis and the phonon density of states of the external modes in rhodochrosite, MnCO3, have been measured by inelastic neutron scattering employing the triple-axis spectrometer at the Dhruva reactor, Trombay. Lattice-dynamics computations based on a transferable potential model reveal the differences in the phonon properties of the isostructural minerals, calcite and rhodochrosite, and their manifestations in various thermodynamic quantities. The calculated dispersion curves and phonon density of states are in good agreement with experiments. The obtained results provide a strong experimental basis to validate the potential model.