The existence of a critical mass ratio for cylinders undergoing vortex-induced vibration (VIV) in a translational system has been well established. Below this critical point, the reduced velocity at VIV lock-out tends to infinity. It has been surmised that a corresponding mass moment of inertia ratio must exist for a pivoted cylinder arrangement. To the authors' knowledge there has been no investigation published substantiating this premise. The aim of the present investigation then was to examine the critical point for cylinders in a rotational system. The approach adopted involved measuring the VIV amplitude response of a positively buoyant, and hence rising, pivoted cylinder at very high reduced velocity. High reduced velocity was attained by establishing a very low system natural frequency through the omission of external restoring forces. The key finding of this study is the presence of a critical point with a value similar to that of the critical mass ratio in translational systems. This critical point does not however appear to be governed by the mass moment of inertia ratio but rather by the force moment ratio.