{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"centripetal-force"},"result":{"entity_type":"calculator","id":"centripetal-force","calculator_id":"centripetal-force","canonical_url":"https://tttkmbb.com/physics/centripetal-force","name":"Centripetal Force Calculator","title":"Centripetal Force Calculator – F = m·v² / r, Acceleration, Angular Velocity and Period","category":"physics","category_name":"Physics","tool_name":"calculate_centripetal_force","featured_mcp_tool":false,"description":"Computes the centripetal (centre-seeking) force and acceleration needed to keep a mass moving in a circle of given radius at a given speed, plus the angular velocity, rotation period and rpm.","use_when":"You need the force on a car in a bend, a mass on a string, a satellite or a centrifuge sample from mass, tangential speed and radius, or the g-load of circular motion.","do_not_use_when":"You know the angular speed (rpm) rather than the tangential speed (compute v = ω·r first), or the motion is not circular at constant speed.","inputs":[{"name":"mass_kg","label":"Mass","type":"number","unit":"kg","required":true,"exclusive_min":0,"description":"Mass of the moving object in kilograms.","example":1200},{"name":"velocity_m_s","label":"Tangential speed","type":"number","unit":"m/s","required":true,"exclusive_min":0,"description":"Speed along the circular path in metres per second.","example":20},{"name":"radius_m","label":"Radius","type":"number","unit":"m","required":true,"exclusive_min":0,"description":"Radius of the circular path in metres.","example":50}],"outputs":[{"name":"centripetal_force_n","label":"Centripetal force","type":"number","unit":"N","decimals":4,"description":"F = m × v² / r, directed toward the centre."},{"name":"centripetal_acceleration_m_s2","label":"Centripetal acceleration","type":"number","unit":"m/s²","decimals":4,"description":"a = v² / r."},{"name":"acceleration_g","label":"Acceleration","type":"number","unit":"g","decimals":4,"description":"Centripetal acceleration in multiples of 9.80665 m/s²."},{"name":"angular_velocity_rad_s","label":"Angular velocity","type":"number","unit":"rad/s","decimals":4,"description":"ω = v / r."},{"name":"period_s","label":"Period","type":"number","unit":"s","decimals":4,"description":"Time for one revolution, 2π r / v."},{"name":"rpm","label":"Revolutions per minute","type":"number","unit":"rpm","decimals":4,"description":"60 / period."}],"input_schema":{"type":"object","properties":{"mass_kg":{"description":"Mass of the moving object in kilograms. 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Unit: rpm.","type":"number","x-unit":"rpm"}}},"formula":"centripetal_acceleration = velocity_m_s² / radius_m; centripetal_force_n = mass_kg × velocity_m_s² / radius_m; ω = velocity_m_s / radius_m; period_s = 2π × radius_m / velocity_m_s; rpm = 60 / period_s","sources":[{"name":"HyperPhysics – Centripetal force","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Centripetal force","url":"https://en.wikipedia.org/wiki/Centripetal_force","type":"reference","retrieved_at":"2026-09-23"},{"name":"NIST CODATA – standard acceleration of gravity g_n = 9.80665 m/s²","url":"https://physics.nist.gov/cgi-bin/cuu/Value?gn","type":"standard","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"1200 kg car at 20 m/s in a 50 m bend","inputs":{"mass_kg":1200,"velocity_m_s":20,"radius_m":50},"expected":{"centripetal_force_n":9600,"centripetal_acceleration_m_s2":8,"acceleration_g":0.8158,"angular_velocity_rad_s":0.4,"period_s":15.708,"rpm":3.8197},"url":"https://tttkmbb.com/api/v1/calculate/centripetal-force?mass_kg=1200&velocity_m_s=20&radius_m=50"},{"name":"0.5 kg on a 0.75 m string at 3 m/s","inputs":{"mass_kg":0.5,"velocity_m_s":3,"radius_m":0.75},"expected":{"centripetal_force_n":6,"centripetal_acceleration_m_s2":12,"angular_velocity_rad_s":4,"period_s":1.5708,"rpm":38.1972},"url":"https://tttkmbb.com/api/v1/calculate/centripetal-force?mass_kg=0.5&velocity_m_s=3&radius_m=0.75"}],"faq":[{"q":"What provides the centripetal force?","a":"Whatever real force points toward the centre: friction for a car in a bend, tension for a string, gravity for a satellite. If that force cannot reach the required value the object leaves the circle."},{"q":"Is centrifugal force the same thing?","a":"Centrifugal force is the apparent outward force felt in the rotating frame; it has the same magnitude as the centripetal force but is not a real force in an inertial frame."}],"tags":["centripetal force","centripetal acceleration","circular motion","angular velocity","rpm","g force"],"related":[{"calculator_id":"newtons-second-law","reason":"Newton's second law in general."},{"calculator_id":"acceleration","reason":"Linear acceleration from velocity change."},{"calculator_id":"circle","reason":"Circumference of the circular path."}],"links":{"html":"https://tttkmbb.com/physics/centripetal-force","markdown":"https://tttkmbb.com/physics/centripetal-force.md","json":"https://tttkmbb.com/physics/centripetal-force.json","api":"https://tttkmbb.com/api/v1/calculate/centripetal-force","schema":"https://tttkmbb.com/api/v1/calculators/centripetal-force","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:30:00Z","next_actions":[{"tool":"run_calculator","calculator_id":"centripetal-force","reason":"Run Centripetal Force Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/physics/centripetal-force.md"}}