The multi-object fiber-fed spectrograph AAOmega at the Anglo-Australian Telescope has been used to establish and measure accurate (<=1km/s) radial velocities for a new sample of members in the outer parts of the stellar system {omega} Centauri. The new sample more than doubles the number of known members with precise velocities that lie between 25' and 45' from the cluster center. Combining this sample with earlier work confirms that the line-of-sight velocity dispersion of {omega} Cen remains approximately constant at ~6.5km/s in the outer parts of the cluster, which contain only a small fraction of the total cluster stellar mass. It is argued that the approximately constant velocity dispersion in the outer regions is most likely a consequence of external influences, such as the tidal shock heating that occurs each time {omega} Cen crosses the Galactic plane. There is therefore no requirement to invoke dark matter or non-standard gravitational theories.