Uniform Circular Motion Calculator

Uniform Circular Motion Calculator. Enter your object's radius, speed, or period to analyze its uniform circular motion. This calculator solves for centripetal acceleration, angular velocity, frequency, period, and centripetal force — give it a mass and it handles the force too. Results pre-render instantly so you can explore how changing the radius or velocity reshapes the motion. Also try the Frequency to Period Converter.

Results

Centripetal Acceleration

Period

Frequency

Angular Velocity

Centripetal Force

Circumference

What is uniform circular motion?

Uniform circular motion is the motion of an object traveling along a circular path at a constant speed. Although the speed is constant, the velocity is not — it continuously changes direction, meaning the object is always accelerating toward the center of the circle. This inward acceleration is called centripetal acceleration. See also our Angular Momentum Calculator.

What is constant in uniform circular motion?

In uniform circular motion, the object's speed (magnitude of velocity) and the radius of the circular path remain constant. The direction of velocity, however, changes continuously — always tangent to the circle. The centripetal acceleration and centripetal force also remain constant in magnitude but change in direction.

How do I calculate centripetal acceleration?

Centripetal acceleration (aₙ) is calculated using the formula aₙ = v² / r, where v is the linear speed and r is the radius of the circular path. For example, an object moving at 10 m/s on a 5 m radius circle has a centripetal acceleration of 100 / 5 = 20 m/s².

What is the relation between linear velocity and angular velocity?

Linear velocity (v) and angular velocity (ω) are related by the equation v = ω × r, where r is the radius. Angular velocity is measured in radians per second (rad/s) and represents how fast the object rotates around the center. Rearranging: ω = v / r. You might also find our calculate Flywheel Energy Storage useful.

What is the centripetal force on an object in circular motion?

Centripetal force is the net inward force required to keep an object moving in a circular path. It is calculated as F = m × aₙ = m × v² / r, where m is the object's mass, v is its speed, and r is the radius. This force is always directed toward the center of the circle.

How are period and frequency related in circular motion?

Period (T) is the time it takes for one complete revolution, while frequency (f) is the number of revolutions per second. They are reciprocals: T = 1 / f and f = 1 / T. Period can also be calculated as T = 2πr / v, where r is the radius and v is the speed.

How do I find angular velocity from period or frequency?

Angular velocity (ω) can be derived from period or frequency using: ω = 2π / T = 2πf. So if the period is 3.14 seconds, ω = 2π / 3.14 ≈ 2 rad/s. Alternatively, if you know the linear speed and radius, ω = v / r.

What are real-world examples of uniform circular motion?

Common examples include a satellite orbiting Earth at constant altitude, a car navigating a circular roundabout at steady speed, the tip of a clock's second hand, and a ball whirled on a string at constant speed. In all cases, the speed is constant but direction changes continuously.