Several observational studies have shown that many Galactic globular clusters (GCs) are characterised by internal rotation. Theoretical studies of the dynamical evolution of rotating clusters have predicted that, during their long-term evolution, these stellar systems should develop a dependence of the rotational velocity around the cluster's centre on the mass of stars, with the internal rotation increasing for more massive stars. In this paper we present the first observational evidence of the predicted rotation-mass trend. In our investigation, we exploited the $\mathit{Gaia}$ Data Release 3 catalogue of three GCs: NGC 104 (47 Tuc), NGC 5139 ($\omega$ Cen) and NGC 5904 (M 5). We found clear evidence of a cluster rotation-mass relation in 47 Tuc and M 5, while in $\omega$ Cen, the dynamically youngest system among the three clusters studied here, no such trend was detected. Comment: 6 pages, 4 figures, 1 table. Accepted for publication in MNRAS Letters
