Horizontal branch stars belong to an advanced stage in the evolution of the oldest stellar galactic population, occurring either as field halo stars or grouped in globular clusters. The discovery of multiple populations in clusters that were previously believed to have single populations gave rise to the currently accepted theory that the hottest horizontal branch members (the 'blue hook' stars, which had late helium-core flash ignition, followed by deep mixing) are the progeny of a helium-rich 'second generation' of stars. It is not known why such a supposedly rare event (a late flash followed by mixing) is so common that the blue hook of ω Centauri contains approximately 30 per cent of the horizontal branch stars in the cluster, or why the blue hook luminosity range in this massive cluster cannot be reproduced by models. Here we report that the presence of helium core masses up to about 0.04 solar masses larger than the core mass resulting from evolution is required to solve the luminosity range problem. We model this by taking into account the dispersion in rotation rates achieved by the progenitors, whose pre-main-sequence accretion disk suffered an early disruption in the dense environment of the cluster's central regions, where second-generation stars form. Rotation may also account for frequent late-flash-mixing events in massive globular clusters.