Moment of Inertia API

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.