We present the results of a survey of radial velocities over a wide region extending from r ~= 10 out to 80 arcmin (~1.5 tidal radii) within the massive star cluster ω Centauri (ω Cen). The survey was performed with FLAMES@VLT, to study the velocity dispersion profile in the outer regions of this stellar system. We derived accurate radial velocities for a sample of 2557 newly observed stars, identifying 318 bona fide cluster red giants. Merging our data with those provided by our previous survey, we assembled a final homogeneous sample of 946 cluster members that allowed us to trace the velocity dispersion profile from the centre out to r ~ 32 arcmin. The velocity dispersion appears to decrease monotonically over this range, from a central value of σv ~ 17.2kms-1 down to a minimum value of σv ~ 5.2kms-1. The observed surface brightness profile, rotation curve, velocity dispersion profile and ellipticity profile are simultaneously well reproduced by a simple dynamical model in which mass follows light, within the classical Newtonian theory of gravitation. The comparison with an N-body model of the evolution of a system mimicking ω Cen during the last 10 orbits into the Galactic potential suggests that (i) the rotation of stars lying in the inner ~=20 arcmin of the clusters is not due to the effects of the tidal field of the Milky Way, as hypothesized by other authors and (ii) the overall observational scenario is still compatible with the possibility that the outer regions of the cluster are subject to some tidal stirring. Based on FORS observations collected with the Very Large Telescope at the European Southern Observatory (ESO), Cerro Paranal, Chile, within the observing programmes 071.D-0217A and 081.D-0255A. E-mail: asollima [at] iac.es (asollima[at]iac[dot]es)