Describing Uniform Circular Motion

When an object travels along a circular path at constant speed, we say it undergoes uniform circular motion. Everyday examples abound: a car rounding a roundabout at steady speed, a point on a spinning fan blade, or the Moon looping around Earth. Although the speed is constant, the motion is far from simple, because the direction of travel is continuously changing. To handle this precisely, physicists describe position using angles rather than only linear distances.

Imagine a particle moving on a circle of radius $r$. Instead of asking how far along the arc it has traveled, we ask through what angle it has turned. This is the angular displacement $\theta$, measured from a chosen reference line drawn from the center. The most convenient unit for angular displacement is the radian. One radia