Beams of light can carry spin and orbital angular momentum. Spin angular momentum describes how the direction of the electric field rotates about the propagation axis, while orbital angular momentum describes the rotation of the field amplitude pattern. These concepts are well understood for monochromatic beams, but previous theoretical studies have constructed polychromatic superpositions where the connection between angular momentum and rotation of the electric field becomes much less clear. These states are superpositions of two states of light carrying opposite signs of angular momentum and slightly detuned frequencies. They rotate at the typically small detuning frequency and thus we call them slowly rotating modes of light. Strangely, some of these modes appear to rotate in the direction opposing the sign of their angular momentum, while others exhibit overall rotation with no angular momentum at all! These findings have been the subject of some controversy, and in 2012, Susanna Todaro (HMC ’12) and I began work on trying to shed light on this “angular momentum paradox." In this thesis, I extend previous work in theory, simulation, and experiment. Via theory and modeling in Mathematica, I present a possible intuitive explanation for the angular momentum paradox. I also present experimental realization of slowly rotating spin superpositions, and outline the steps necessary to generate slowly rotating orbital angular momentum superpositions.