Ideal rigid-body mechanics — arithmetic check
Flywheel Rotational Energy Arithmetic
Compute stored rotational kinetic energy from a documented moment of inertia or one of two explicitly idealized geometries. This is not a safe-speed,stress or containment calculation.
Résultat arithmétique
Implemented arithmetic
E=½Jω²
uniform solid disk:J=½mR²
ideal thin ring:J=mR²
Here n is in revolutions per minute,ω in radians per second,J in kg·m²,m in kg,R in metres and E in joules. The disk and ring equations apply only to the stated uniform idealizations rotating about the central symmetry axis. Use direct J for any other geometry,with its source documented.
Mechanics and unit sources
MIT OpenCourseWare,Classical Mechanics §16.3 gives rotational kinetic energy and the uniform-disk central-axis inertia. OpenStax University Physics §11.2 derives J=mR² for a thin hoop. NIST SP811 AppendixB.8 gives lb·ft²→kg·m²,kWh→J and mechanical-horsepower relationships. The implementation uses exact definitions:1lb=0.45359237kg,1ft=0.3048m,1in=0.0254m,1kWh=3,600,000J and1mechanical hp=745.69987158227022W.
What the result does not mean
Stored energy is not automatically deliverable energy. Losses,maximum/minimum operating speeds and conversion efficiency are external. A safe flywheel speed cannot be inferred from one generic hoop-stress equation:real stress depends on geometry,material model,temperature,manufacturing defects,stress concentrations,fatigue,fracture behavior,attachments and containment requirements.
