This paper presents an analysis of a model problem, consisting of two interacting rigid rings, for the rotation of molecules in liquid He-4. Due to Bose symmetry, the excitation of the rotor corresponding to a ring of N helium atoms is restricted to states with integer multiples of N quanta of angular momentum. This minimal model shares many of the same features of the rotational spectra that have been observed for molecules in nanodroplets of approximate to 10(3)-10(4) helium atoms. In particular, this model predicts, for the first time, the very large enhancements of the centrifugal distortion constants that have been observed experimentally. It also illustrates the different effects of increasing rotational velocity by increases in the angular momentum quantum number or by increasing the rotational constant of the molecular rotor. It is found that a fixed node, diffusion Monte Carlo and a hydrodynamic model provide upper and lower bounds respectively on the size of the effective rotational constant of the molecular rotor when coupled to the helium. (C) 2001 American Institute of Physics.