Classical Mechanics

Circular Motion Calculator

Calculate centripetal acceleration, centripetal force, angular velocity and orbital period for any circular motion — from satellites to roundabouts.

Inputs

a_c = v²/r · F_c = mv²/r

ω = v/r · T = 2π/ω

Mass

Radius

Examples

Enter mass, radius and speed (or period) to calculate.

Circular motion equations

Centripetal acceleration

a_c = v²/r = ω²r

Centripetal force

F_c = mv²/r = mω²r

Angular velocity

ω = v/r = 2π/T = 2πf

Period

T = 2πr/v = 2π/ω

Speed from period

v = 2πr/T = ωr

Frequency

f = 1/T = ω/(2π)

Circular motion and centripetal force

Any object moving in a circle is constantly accelerating — not because its speed changes, but because its direction changes. This centripetal acceleration always points toward the centre of the circle and equals v²/r. The centripetal force F = mv²/r is the net force required to maintain this circular path — it is provided by gravity (for satellites), tension (for a ball on a string), friction (for a car on a road), or a normal force (for a loop-the-loop).

Centripetal force is not a new type of force — it is the name for whatever force keeps the object on its circular path. See our article on Circular Motion and Centripetal Force.

What is the difference between centripetal and centrifugal force?↓

Centripetal force is real — it acts on the rotating object toward the centre. Centrifugal force is a fictitious force that appears to push outward in the rotating reference frame. In an inertial frame, there is no centrifugal force; the object's tendency to 'fly outward' is simply inertia.

Why does orbital speed decrease with radius?↓

From F_c = mv²/r, if the gravitational force F = GMm/r² provides the centripetal force, then v = √(GM/r). Larger orbit radius means lower orbital speed — but longer circumference, so the period increases even faster (T ∝ r^(3/2), Kepler's third law).

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