The Bohr-Mottelson collective model is central to the study of nuclear structure physics. The model treats nuclei as ellipsoids and focuses on their vibrational and rotational degrees of freedom. The rotational part of the model regards the moment of inertia of the nuclei as a falling between the extreme of a rigid body and an irrotational fluid. The true moment of inertia, as revealed by experiment, provides a parameter between these two extremes and acts as a way of interpolating the data. In this work, we show how the interpolating parameter between the two extreme moments of inertia can be treated theoretically using an algebraic and differential geometric framework. The essential idea is to couple the angular momentum of the nucleus with a ``magnetic" term that involves the Kelvin circulation into a covariant derivative. This coupling term or connection can be found by solving a Yang-Mills equation. Measuring the nuclear Kelvin circulation then reveals a theoretical justification for the determining the correct moment of inertia.