A rotating superconductor exhibits various physical effects, however, the dynamics of rotating vortices remain relatively unexplored. A solid theoretical foundation is the necessary precursor for experimental validation and application. This work presents key mathematical findings, including an approximation for the number of single-fluxon pinning sites in the superconductor and the dependence of the quantum fluxon on the bulk rotation leading to the quantization of the London moment. These results were derived from the superfluid-analogous behavior of supercurrents and the Abrikosov magnetic field structure. Beyond fundamental theory, this study shows that the rotation dependence can then be applied to multi-input logic gates for vortex based computation. In particular, vortex motion patterns and pinning energies are found to vary with rotation and thus shown to mimic neural network behavior. Arrays of variable vortex pinning sites were simulated, and their rotation-sensitive responses were perturbed with small currents to train a machine learning algorithm in recognizing vortex configurations patterns, similar to how biological neurons adapt yet surpassing traditional computing systems. Unlike established vortex computation systems, the recognition and control of rotation as an input provides greater flexibility and thus increased possibilities for application from classical to quantum computing.