While a single Carroll particle can not move, a multiparticle system with momentum-dependent interaction \underline{can}: the center-of-mass is fixed however relative motion is possible, confirming a previous statement made by Bergshoeff et al \cite{Bergshoeff14}. Analogous results are obtained for electric dipoles with the roles of the center-of-mass and the relative position interchanged. Immobility can also be deduced from the Carroll boost symmetry.