Young star clusters enable us to study the effects of stellar rotation on an ensemble of stars of the same age and across a wide range in stellar mass and are therefore ideal targets for understanding the consequences of rotation on stellar evolution. We combine MUSE spectroscopy with HST photometry to measure the projected rotational velocities (Vsini) of 2184 stars along the split main sequence and on the main sequence turn-off (MSTO) of the 100Myr-old massive (10^5^M_{sun}_) star cluster NGC 1850 in the Large Magellanic Cloud. At fixed magnitude, we observe a clear correlation between Vsini and colour, in the sense that fast rotators appear redder. The average Vsini values for stars on the blue and red branches of the split main sequence are ~100km/s and ~200km/s, respectively. The values correspond to about 25-30% and 50-60% of the critical rotation velocity and imply that rotation rates comparable to those observed in field stars of similar masses can explain the split main sequence. Our spectroscopic sample contains a rich population of ~200 fast rotating Be stars. The presence of shell features suggests that 23% of them are observed through their decretion disks, corresponding to a disk opening angle of 15 degrees. These shell stars can significantly alter the shape of the MSTO, hence care should be taken when interpreting this photometric feature. Overall, our findings impact our understanding of the evolution of young massive clusters and provide new observational constraints for testing stellar evolutionary models.