Context. Stellar kinematics in the external regions of globular clusters can be used to probe the validity of Newton's law in the low acceleration regimes without the complication of non-baryonic dark matter. Indeed, in contrast to the case of galaxies, in globular clusters a systematic deviation of the velocity dispersion profile from the expected Keplerian falloff would be indicative of a breakdown of Newtonian dynamics rather than the existence of dark matter. Aims: We perform a detailed analysis of the velocity dispersion in the globular cluster ω Centauri to determine whether it decreases monotonically with distance as expected within the framework of Newtonian dynamics, or whether it converges toward a constant value as recent works suggest. Methods: We combine measurements from two previous studies to almost double the data available at large radii, to better constrain the velocity dispersion profile in the low acceleration regime. Results: We found the inner region of ω Centauri is clearly rotating, while the rotational velocity tends to vanish, being consistent with no rotation at all in the external regions. The cluster velocity dispersion at large radii from the center is found to clearly deviate from the Newtonian prediction. Conclusions: We conclude that there are strong similarities between globular clusters and elliptical galaxies, for in both classes of objects the velocity dispersion tends to remain constant at large radii. In the case of galaxies, this is ascribed to the existence of a massive halo of dark matter, which is physically unlikely in the case of globular clusters. This similarity, if confirmed, is best explained by a breakdown of Newtonian dynamics below a critical acceleration. Tables 2 and 3 are only available in electronic form at http://www.aanda.org