Circular Motion Calculator

Use the circular motion calculator to determine the parameters like frequency, speed, angular velocity, and centripetal acceleration.

Centripetal force5.4 kN1,200 kg × 4.5 m/s²

Centripetal acceleration4.5 m/s²0.4589 g

Speed15 m/s54 km/h

Angular velocity0.3 rad/s2.865 rpm

Period of one revolution20.943951 s

Frequency0.047746 Hz

Maximum speed friction can hold19.8057 m/s71.3 km/h — √(µgr), with no mass term, so a loaded and an empty vehicle corner at the same limit

Your speed against that limit75.74%within grip

Friction available9.4144 kNagainst 5.4 kN needed

Bank angle needing no friction24.649°arctan(v²/rg) — on a track banked this steeply the turn holds on a frictionless surface

At twice the speed21.6 kNfour times the force — it goes as the square of speed, which is why corners punish speed so hard

At twice the radius2.7 kNhalf the force, at the same speed

The formula

a = v²/r = ω²r; F = ma

There is no centrifugal force

Circular motion needs a force pointing inward, because the velocity is constantly changing direction and that change is an acceleration towards the centre. For a car it is friction, for a satellite gravity, for a ball on a string the tension.

The outward "centrifugal force" you feel is not a force acting on you at all. It is your own inertia: your body continues straight while the car turns, and the door pushes you inward. In the rotating frame of the car it is convenient to treat that as an outward force, and doing so gives correct answers — but nothing is pulling you outward, which is why the sensation vanishes the instant the constraint does. Let go of the string and the ball flies off along a tangent, not radially outward.

The grip limit √(µgr) contains no mass, so a loaded lorry and an empty one slide at the same cornering speed — extra weight increases both the required force and the available friction in equal measure. Banking the road tilts the normal force inward so it supplies the turn directly, which is why racing circuits and railway curves are banked.