A very simple model of a diatomic molecule—a rigid dumbbell‐flywheel system—is used to illustrate the close relationship between molecular dynamics and gauge fields. It is shown that, under the adiabatic approximation and certain assumptions, even a simple classical analysis yields a Lorentz force in nuclear dynamics due to a magnetic monopole gauge field. This classical treatment, however, fails to explain the origin of the ‘‘magnetic’’ force. An exact quantum mechanical treatment based on relinquishing the Born–Oppenheimer approximation reveals unambiguously both the origin and the nature of the monopole gauge potential, justifies the adiabatic approximation, and yields an expression for the energy eigenvalues. We believe this simple and exactly solvable model is not only suitable as a pedagogical tool for molecular dynamics, but also ideal for communicating some aspects of the physics behind gauge field theories to advanced undergraduates.