Uniform circular motion occurs when an object moves in a circular path at a constant speed. Although the speed is constant, the velocity continuously changes direction, meaning the object experiences centripetal acceleration directed toward the center of the circle. This acceleration is caused by a net centripetal force.

Centripetal force (F_c) is calculated using F_c = mv²/r, where m is mass, v is tangential velocity, and r is the radius. Alternatively, you can use F_c = mω²r if you know the angular velocity ω. Our calculator automatically computes centripetal force when you provide mass along with at least two motion parameters.

Angular velocity (ω) measures how fast an object rotates, expressed in radians per second (rad/s). Tangential velocity (v) is the linear speed along the circular path, measured in m/s. They are related by v = ω × r. For a given angular velocity, a larger radius produces a higher tangential speed.

You need at least two independent kinematic parameters to fully determine uniform circular motion. For example, knowing the radius (r) and angular velocity (ω), or radius (r) and period (T), is sufficient. Our calculator works with any combination of two parameters among radius, velocity, angular velocity, period, and frequency. Mass is optional and only needed for force calculation.

Circular motion principles apply to planetary orbits, car tires rotating, centrifuges in laboratories, clothes spinning in washing machines, satellites orbiting Earth, amusement park rides (like merry-go-rounds and roller coaster loops), and the motion of charged particles in magnetic fields. Engineers use these calculations to design safe curves on roads and determine structural requirements for rotating machinery.

In uniform circular motion, the object's velocity vector constantly changes direction while maintaining constant magnitude. The change in velocity (Δv) always points toward the center of the circle. Since acceleration is the rate of change of velocity, centripetal acceleration must also point toward the center. This inward acceleration keeps the object moving in a circle rather than flying off in a straight line (which Newton's First Law would otherwise require).

If the centripetal force vanishes instantly (e.g., a string breaks while swinging a ball), the object will fly off tangentially in a straight line at its current velocity, following Newton's First Law of inertia. This is why you see sparks fly tangentially from a grinding wheel or why a car loses control on an icy curve — the friction providing centripetal force is insufficient.

Our RPM (revolutions per minute) values are mathematically exact conversions from the calculated frequency and angular velocity. RPM = f × 60 (from frequency in Hz) or RPM = ω × 60/(2π) (from angular velocity in rad/s). The displayed values are rounded to 2 decimal places for clarity, but internal calculations maintain high precision.