We report on the results of an i-band time-series photometric survey of NGC2516 using the Cerro Tololo Inter-American Observatory (CTIO) 4-m Blanco telescope and 8k Mosaic-II detector, achieving better than 1 per cent photometric precision per data point over 15 <~ i <~ 19. Candidate cluster members were selected from a V versus V - I colour-magnitude diagram over 16 < V < 26 (covering masses from 0.7Msolar down to below the brown dwarf limit), finding 1685 candidates, of which we expect ~1000 to be real cluster members, taking into account contamination from the field (which is most severe at the extremes of our mass range). Searching for periodic variations in these gave 362 detections over the mass range 0.15 <~ M/Msolar <~ 0.7. The rotation period distributions were found to show a remarkable morphology as a function of mass, with the fastest rotators bounded by P > 0.25d, and the slowest rotators for M <~ 0.5Msolar bounded by a line of P ~ M3, with those for M >~ 0.5Msolar following a flatter relation closer to P ~ constant. Models of the rotational evolution were investigated, finding that the evolution of the fastest rotators was well reproduced by a conventional solid body model with a mass-dependent saturation velocity, whereas core-envelope decoupling was needed to reproduce the evolution of the slowest rotators. None of our models were able to simultaneously reproduce the behaviour of both populations.