Increasing numbers of floating offshore wind turbines (FOWTs) are planned in the coming years due to their high potential in the massive generation of clean energy from ocean wind. In the present study, a numerical prediction tool has been developed for the fully coupled dynamic analysis of an FOWT system in the time domain including aero-loading, tower/blade elasticity, blade-rotor dynamics and control, mooring dynamics, and platform motions so that the influence of aero-elastic-control dynamics on the hull-mooring performance and vice versa can be assessed. The Hywind spar design with a 5MW National Renewable Energy Laboratory (NREL) turbine is selected as an example and two different collinear wind-wave-current environmental conditions, maximum operational and survival conditions, are applied for this study. The maximum operational condition means the maximum environmental condition with normal blade-turbine operation and the survival condition represents the extreme situation without any blade-turbine operation. Through this study, it is seen that the ultimate-loading environments for different structural components of the FOWT can be different. The developed technology and numerical tool are readily applicable to the design of any type of future FOWTs in any combinations of irregular waves, dynamic winds, and steady currents.