The aim of the present investigation was to examine the critical vortex-induced vibration (VIV) point for cylinders in a rotational system. For translational systems, the existence of a critical mass ratio for cylinders undergoing vortex-induced vibration has been well established. At mass ratios below this critical point, the reduced velocity at VIV lock-out tends to infinity, resulting in the resonance forever condition as described by the authors first reporting this phenomenon. The approach adopted in the present investigation involved measuring the VIV response of a positively buoyant pivoted cylinder being towed at very high reduced velocity. High reduced velocity was attained by establishing a very low system natural frequency. 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 appears to be governed by the force moment ratio rather than the mass moment of inertia ratio. In the present study, a critical force moment ratio of 0.512 ± 0.002 was determined as the onset point for the infinite VIV lock-in regime.