Circular Motion Calculator
Uniform circular motion occurs when an object moves along a circular path at constant speed. Although the speed is constant, the velocity continually changes direction, requiring a centripetal acceleration directed toward the center. This calculator computes all key properties of uniform circular motion from the radius and either the period or tangential velocity.
For an object in uniform circular motion with radius r and period T, the key relationships are: v = 2πr/T (tangential velocity), f = 1/T (frequency), ω = 2π/T (angular velocity), and a = v²/r = 4π²r/T² (centripetal acceleration).
The centripetal acceleration always points toward the center of the circle. Without a centripetal force to produce this acceleration, the object would fly off in a straight line (Newton’s first law). The source of centripetal force varies: gravity for orbiting bodies, tension for a ball on a string, friction for a car rounding a curve, and the normal force for a roller coaster loop.
Circular motion analysis is essential in orbital mechanics (satellites, planets), rotating machinery (turbines, centrifuges), particle accelerators, amusement park ride design, and vehicle dynamics. Any system involving rotation or curved paths relies on these fundamental relationships.