Kinetic Energy & Moment of Inertia • Hoop Stress • Materials — Simulate • Explore • Practice • Quiz
Flywheel energy storage systems store energy in the form of rotational kinetic energy by spinning a massive rotor (flywheel) at high angular velocities. This technology has been used for centuries — from potter's wheels to modern grid-scale energy storage, uninterruptible power supplies (UPS), and regenerative braking in hybrid vehicles. The key advantage of flywheel storage is its ability to absorb and release energy very quickly, making it ideal for high-power, short-duration applications.
A flywheel stores energy according to the equation KE = ½Iω², where I is the moment of inertia and ω is the angular velocity. To maximise stored energy, engineers either increase the mass and radius (increasing I) or spin the flywheel faster (increasing ω). Since energy scales with the square of angular velocity, high-speed flywheels using advanced composite materials can achieve remarkable energy densities.
The moment of inertia depends on the mass distribution relative to the axis of rotation. For a solid disk, I = ½mr². For a thin ring or hollow cylinder, I = ½m(r&sub1;² + r&sub2;²), where r&sub1; and r&sub2; are the inner and outer radii. Ring-type flywheels concentrate mass at the rim, giving a higher moment of inertia per unit mass — this is why most high-performance flywheels use a ring or rim design.
The maximum rotational speed of a flywheel is limited by the hoop stress σ = ρω²r², where ρ is the material density. Steel flywheels are limited to tip speeds of about 200–300 m/s, while carbon fibre composite flywheels can exceed 1000 m/s due to their superior strength-to-density ratio. Common materials include steel (ρ ≈ 7850 kg/m³, σ_yield ≈ 250–600 MPa), aluminium (ρ ≈ 2700 kg/m³, σ_yield ≈ 270 MPa), and carbon fibre composites (ρ ≈ 1600 kg/m³, σ_tensile ≈ 1500–2500 MPa).
In Simulate mode, select a flywheel type (Solid Disk, Ring, or Spoke), choose a material, then adjust mass, radii, and RPM using the sliders. The canvas shows an animated rotating flywheel with real-time energy gauge and cross-section. Readout cards display moment of inertia, kinetic energy, angular velocity, hoop stress, energy density, tip speed, and safety factor. Switch to Explore mode to study 10 concepts across Basics, Design, and Performance. Practice mode generates random flywheel problems, and Quiz tests your knowledge with 5 randomised questions.
This simulator is designed for mechanical engineering students, energy systems trainees, dynamics and machine design students, and instructors teaching rotational energy storage, flywheel design, and material selection for high-speed rotating machinery.