Energy storage is important for many applications from hybrid vehicles to off-peak electric power to rotating machinery. A flywheel offers the combination of high energy density and high power density not attainable with other energy storage medium. In many situations, it is desirable to store energy at a constant angular velocity. This work proposes a novel self-governing fluidic variable inertia flywheel that can maintain a constant angular velocity across a range of energy storage. The fluidic flywheel uses a piston to separate the liquid filled chamber from a chamber vented to atmosphere. A force balance is created on the piston due to the radial pressure gradient of the liquid reacted by a constant force spring. Energy added to the system is stored in equally two forms: increases the kinetic energy of the flywheel at a constant angular velocity and increasing the potential energy of the constant force spring. A design example demonstrates that the fluidic flywheel enables a constant angular velocity with an order of magnitude lower mass moment of inertia than a conventional flywheel. This promising technology enables a simple constant angular velocity energy storage system, yet requires future work in numerous areas.