Uniform Circular Motion

In uniform circular motion, speed remains constant but direction continuously changes. Since acceleration is any change in velocity—including direction—the object accelerates radially inward toward the circle's center. This inward acceleration, called centripetal acceleration, occurs even though speed is constant because velocity is a vector quantity affected by directional changes.

Centripetal acceleration is the radial acceleration directed toward the center of a circular path. Its magnitude equals the square of the object's velocity divided by its distance from the center. For a satellite orbiting Earth, this acceleration is provided by gravitational force. The relationship can also be expressed using the orbital period and circumference.

In uniform circular motion, the linear velocity is always tangential to the circular path. While the magnitude of velocity remains constant, its direction continuously changes as the object moves around the circle. This constant change in direction is what produces the centripetal acceleration toward the center.

A centripetal force directed toward the center of the circle maintains uniform circular motion. For orbiting satellites, Earth's gravitational force provides this centripetal force. The centripetal force is always perpendicular to the velocity and causes the radial acceleration that keeps the object moving in its circular path.

Centripetal acceleration depends on both the object's speed and the radius of its circular path. Acceleration increases with the square of the speed and decreases with larger radius. This relationship means that faster motion or tighter curves produce greater centripetal acceleration, requiring stronger inward forces.

Orbital period T relates to centripetal acceleration through the circular path's circumference, 2πr. Since speed equals circumference divided by period, substituting this into the centripetal acceleration formula yields a relationship between acceleration and the satellite's orbital period, allowing prediction of motion characteristics.

Common examples include points on a propeller spinning at constant rate, watch hands, and orbiting satellites. Any object traveling in a circle at constant speed exhibits uniform circular motion. These examples demonstrate that even with constant rotation rates, points on rotating objects experience centripetal acceleration directed toward the center.