Circular motion
Circular motion is movement of an object along a circular path. In uniform circular motion the speed is constant, but the velocity's direction constantly changes, requiring a centripetal acceleration a = v²/r directed toward the center.
Circular motion is motion along a circular path. In uniform circular motion, the object's speed is constant — yet it is still accelerating, because velocity is a vector and its direction changes at every instant. That acceleration, called centripetal acceleration, always points toward the center of the circle and has magnitude a = v²/r, where v is the speed and r is the radius.
By Newton's second law, this acceleration requires a net inward force: F = mv²/r. Crucially, centripetal force is not a new kind of force — it is whatever real force (or combination) points toward the center. For a ball on a string it is tension; for a car rounding a flat curve it is friction; for a satellite it is gravity; for clothes in a spinning dryer drum it is the normal force. If the inward force disappears, the object flies off in a straight line along the tangent — not outward.
A worked example: a 1,000 kg car takes a curve of radius 50 m at 20 m/s. The required centripetal force is F = (1,000 × 20²) / 50 = 8,000 N, which friction must supply; if the road is icy and friction cannot provide 8,000 N, the car slides wide. Related quantities include period (time per revolution) and the relation v = 2πr/T.
Circular motion is tested across the sciences. The AP Physics 1 exam emphasizes free-body diagrams for objects in vertical and horizontal circles, the MCAT tests centripetal force conceptually within translational motion and forces, and the FE Civil exam applies the same relations in its dynamics coverage of curvilinear motion.
Key takeaways
- An object in uniform circular motion has constant speed but continuously changing velocity direction, so it accelerates toward the center.
- Centripetal acceleration is a = v²/r, and the required net inward force is F = mv²/r.
- Centripetal force is supplied by real forces — tension, friction, gravity, or the normal force — not a separate force of its own.
- Without an inward force, the object moves off along the tangent in a straight line.
- AP Physics 1, the MCAT, and the FE Civil exam all test circular motion and centripetal force.