Centripetal force & circular motion API

Computes centripetal acceleration a=v²/r=ω²·r and force F=m·v²/r for uniform circular motion, plus angular velocity, period, rpm, and the frictionless banking angle. Answers 'What is the centripetal force on a car in a turn?', 'What banking angle is needed for a curve?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/centripetal-force

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

engineeringmechanicsphysicscentripetal-forcecircular-motionbanking-angleangular-velocityrotation

API URLhttps://x402.hexl.dev/v1/engineering/centripetal-force

Integration docs

Example request

{
  "massKg": 1000,
  "radiusM": 50,
  "velocityMs": 20
}

Example response

{
  "radiusM": 50,
  "velocityMs": 20,
  "angularVelocityRadS": 0.4,
  "centripetalAccelerationMs2": 8,
  "periodS": 15.707963,
  "rpm": 3.819719,
  "bankingAngleDeg": 39.2066,
  "formula": "a = v²/r = ω²*r, F = m*v²/r, tanθ_bank = v²/(r*g)",
  "massKg": 1000,
  "centripetalForceN": 8000
}

Input schema

{
  "type": "object",
  "required": [
    "radiusM"
  ],
  "properties": {
    "radiusM": {
      "type": "number",
      "description": "circular path radius (m)",
      "examples": [
        50
      ]
    },
    "velocityMs": {
      "type": "number",
      "description": "tangential speed (m/s)"
    },
    "angularVelocityRadS": {
      "type": "number",
      "description": "angular velocity ω (rad/s); supply instead of velocity"
    },
    "massKg": {
      "type": "number",
      "description": "mass (kg) for force"
    },
    "gravity": {
      "type": "number",
      "description": "gravity (m/s^2), default 9.80665"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}