#moment-of-inertia

Rigid-body rotational-inertia mechanics as an API, computed locally and deterministically. The shape endpoint returns the mass moment of inertia and the radius of gyration k = √(I/m) for a named standard body about its characteristic axis — a solid sphere (I = 2/5·m·r²), thin spherical shell (2/3·m·r²), solid cylinder or disk (1/2·m·r²), annular/hollow cylinder (1/2·m·(r1²+r2²)), thin ring (m·r²), thin rod about its centre (1/12·m·l²) or about one end (1/3·m·l²), rectangular plate or cuboid (1/12·m·(a²+b²)), solid cone (3/10·m·r²) and point mass (m·r²) — so a 2 kg solid sphere of radius 0.5 m has I = 0.2 kg·m². The parallel-axis endpoint applies the Steiner theorem I = I_cm + m·d² to shift a moment of inertia from the centre-of-mass axis to any parallel axis a distance d away. The shapes endpoint lists the whole catalog with its formulas. All quantities are SI (kg, m → kg·m²). Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-engineering, robotics, CAD/CAE, rotating-machinery, structural-dynamics and physics-education app developers, flywheel-and-shaft design tools, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is rotational inertia; for stored rotational energy and flywheel sizing use a flywheel API and for torque and angular acceleration a torque API.

api.oanor.com/momentofinertia-api

Flywheel and rotational-energy dynamics as an API, computed locally and deterministically. The energy endpoint computes the rotational kinetic energy stored in a spinning body, E = ½·I·ω², together with its angular momentum L = I·ω, in joules, kilojoules and watt-hours — from a moment of inertia (given directly, or worked out from a shape, mass and dimension) and an angular speed given as rpm, radians per second or hertz, which it reports in all three. The inertia endpoint returns the moment of inertia about the central axis for the common shapes — solid disk and cylinder (½·m·r²), thin ring and hoop (m·r²), hollow cylinder (½·m·(r_out²+r_in²)), solid sphere (⅖·m·r²), hollow sphere (⅔·m·r²) and a rod about its centre (1/12·m·L²) or end (⅓·m·L²) — from a mass and a radius, diameter or length. The flywheel endpoint sizes a flywheel: give a target energy and an operating speed and it returns the required inertia I = 2E/ω², or give an inertia and a maximum and minimum rpm and it returns the energy delivered between them, ΔE = ½·I·(ω₁²−ω₂²), with the coefficient of fluctuation. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-engineering and energy-storage tools, motor, engine and powertrain design, kinetic-energy-recovery and physics-education apps. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is rotational energy and inertia; for bolt tightening torque use a torque API and for power-screw mechanics use a screw-jack API.

api.oanor.com/flywheel-api