We study the dynamics and explore the controllability of a family of sphere-plate mechanical systems. These are nonholonomic systems with a five-dimensional (5-D) configuration space and three independent velocities. They consist of a sphere rolling in contact with two horizontal plates. Kinematic models of sphere-plate systems have played an important role in the control systems literature addressing the kinematics of rolling bodies, as well as in discussions of nonholonomic systems. However, kinematic analysis falls short of allowing one to understand the dynamic behavior of such systems, In this work, we formulate and study a dynamic model for a class of sphere-plate systems in order to answer the question: "is it possible to impart a net angular momentum to a sphere which rolls without slipping between two plates, given that the position of the top plate is subject to exogenous forces?"