Flywheel - Physics

Physics

A flywheel is a spinning wheel or disc with a fixed axle so that rotation is only about one axis. Energy is stored in the rotor as kinetic energy, or more specifically, rotational energy:

Where:

• ω is the angular velocity, and
• is the moment of inertia of the mass about the center of rotation. The moment of inertia is the measure of resistance to torque applied on a spinning object (i.e. the higher the moment of inertia, the slower it will spin when a given force is applied).

• The moment of inertia for a solid cylinder is ,
• for a thin-walled empty cylinder is ,
• and for a thick-walled empty cylinder is ,

Where m denotes mass, and r denotes a radius.

When calculating with SI units, the standards would be for mass, kilograms; for radius, meters; and for angular velocity, radians per second. The resulting answer would be in joules.

The amount of energy that can safely be stored in the rotor depends on the point at which the rotor will warp or shatter. The hoop stress on the rotor is a major consideration in the design of a flywheel energy storage system.

Where:

• is the tensile stress on the rim of the cylinder
• is the density of the cylinder
• is the radius of the cylinder, and
• is the angular velocity of the cylinder.

This formula can also be simplified using specific tensile strength and tangent velocity:

Where:

• is the specific tensile strength of the material
• is the tangent velocity of the rim.