This paper presents a futuristic transportation mean: a monorail tramway, running on a narrow rail, stabilized by an inertia wheel. As the required infrastructure is very light, this transportation mean is an interesting answer to traffic saturation problems at which the agglomerations are exposed. To keep its balance, this tramway uses an inertial wheel controlled in real time, and driven by a regenerative actuator and driver, for consumption purpose. This paper is a preliminary study for this project. The analysis of the dynamics of the tramway in the transversal plane is made. The demonstration of the stabilization concept feasibility is done using the inverted pendulum, the most popular tool of the control theory, and more particularly, the inverted inertia wheel pendulum. The mechanical principles used here are classical but unique for this kind of application. Unlike in the other studies of inertia wheel pendulums, the localizations of the centers of masses were decided taking into account the real mass distribution (passengers and the tram structure) and optimized to minimize power consumption. Additionally, instead of using an encoder to measure the orientation of the pendulum, an inclinometer was preferred. Concerning the control part, the Linear Quadratic Gaussian control was chosen to stabilize the inverted pendulum because this control law allows controlling a system even with a partial knowledge of its state. A discussion regarding state observability is carried out showing that, even if in theory the angular velocity of the inertia wheel is enough to observe the full state of the system, in practice a sensor able to measure the orientation of the pendulum needs to be added. Experimental results are given.