Centripetal

Centripetal is a term used to describe something directed toward the center of a circle or curved path. In physics, it most often refers to the inward acceleration that keeps an object moving along a circular trajectory.

Centripetal acceleration a_c is defined as a_c = v^2 / r, where v is speed and r is the radius of the circular path. Using angular velocity ω, a_c can also be expressed as a_c = ω^2 r. The acceleration points toward the center of the circle and is always perpendicular to the object's instantaneous velocity.

Centripetal force is the net inward force that produces centripetal acceleration, given by F_c = m a_c = m v^2 / r. There is no separate physical type of force called “centripetal”; rather, centripetal force is the inward component of the net force acting on the object in circular motion. Examples include gravity providing the inward pull for orbital motion, tension in a string or rod, and static friction between tires and the road when a vehicle turns.

Distinctions are important: in an inertial (non-rotating) frame, centripetal force is the actual inward force. In a rotating reference frame, an outward centrifugal force appears as a fictitious force, but centripetal acceleration remains the real inward acceleration toward the center.

Circular motion can occur at constant speed, yielding only centripetal (radial) acceleration toward the center. If the speed changes, a tangential component of acceleration arises in addition to the centripetal component.