Projectile motion is one important example of motion in a plane. Another quite different type of motion in a plane is circular motion. FIGURE 4.21 shows a particle moving around a circle of radius r. The particle might be a satellite in an orbit, a ball on the end of a string, or even just a dot painted on the side of a rotating wheel.

FIGURE 4.21 A particle in uniform circular motion.

To begin the study of circular motion, consider a particle that moves at constant speed around a circle of radius r. This is called uniform circular motion. Regardless of what the particle represents, its velocity vector $\vec{v}$ is always tangent to the circle. The particle’s speed $v$ is constant, so vector $\vec{v}$ is always the same length.

The time interval it takes the particle to go around the circle once, completing one revolution (abbreviated rev), is called the period of the motion. Period is represented by the symbol T. It’s easy to relate the particle’s period T to its speed $v$. For a particle moving with constant speed, speed is simply distance/time. In one period, the particle moves once around a circle of radius r and travels the circumference $2\pi r$. Thus