#circular-motion

Uniform circular-motion physics as an API, computed locally and deterministically. The centripetal-force endpoint computes the centripetal acceleration a = v²/r = ω²·r — always pointing toward the centre — and the centripetal force F = m·a that holds a body on its circular path, from the mass, the radius and either the linear or the angular velocity, and reports the equivalent g-force. The angular endpoint converts between every way of describing rotation — angular velocity (rad/s), revolutions per minute, frequency, period and, given a radius, the linear (tangential) velocity — using ω = 2π·f = 2π/T = v/r. The centrifuge endpoint computes the relative centrifugal force (RCF, in g) of a centrifuge rotor from its speed in rpm and radius, RCF = ω²·r / g, or inverts it to give the rpm needed to reach a target RCF. Masses are in kg, radii in m (mm for the centrifuge), velocities in m/s, angular velocities in rad/s and forces in N. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education, mechanical, automotive, lab-centrifuge and amusement-ride app developers, rotational-motion and g-force tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is uniform circular motion; for gravitational orbits use a gravitation API, for a vehicle on a banked curve a banked-curve API and for pendulum oscillation a pendulum API.

api.oanor.com/centripetal-api

Banked-curve and circular-motion dynamics as an API, computed locally and deterministically. The speed endpoint takes the radius of a curve and its banking (bank) angle and returns the frictionless ideal (design) speed at which the banking alone supplies the centripetal force, v = √(r·g·tanθ); give a coefficient of friction as well and it also returns the maximum safe speed before the vehicle slides outward up the bank, v = √(r·g·(tanθ+μ)/(1−μ·tanθ)), and the minimum speed before it slides inward down the bank — every speed in metres per second, km/h, mph and knots, plus the centripetal acceleration. The bank-angle endpoint inverts this: from a design speed and radius it returns the ideal banking angle θ = atan(v²/(r·g)) and the equivalent superelevation as a ratio and a percentage, the cant a road or railway needs so no side friction is used at that speed. The flat-curve endpoint handles an unbanked curve from the coefficient of friction: the maximum cornering speed v = √(μ·r·g) for a given radius and the minimum radius v²/(μ·g) for a given speed. Gravity defaults to standard 9.80665 m/s² and can be overridden. Everything is computed locally and deterministically, so it is instant and private. Ideal for road and racetrack design tools, vehicle-dynamics and driving-simulator apps, civil and transportation engineering, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is curve banking and cornering dynamics; for projectile and SUVAT kinematics use a physics API.

api.oanor.com/bankedcurve-api