Zentripetal

Zentripetal is a term used in German-language physics to describe inward-directed forces and accelerations that keep an object moving along a circular path. In English literature the corresponding concept is centripetal. The term is often used in discussions of circular motion and the dynamics that sustain it.

Mathematically, if an object of mass m moves with speed v along a circle of radius r, the required acceleration toward the center is a_c = v^2 / r, directed toward the circle's center. The centripetal (Zentripetal) force F_c equals m a_c and is provided by whatever keeps the object in circular motion (tension in a string, friction between tires and road, gravitational attraction, etc.). In vector form, the force is always directed radially inward toward the center of the circle.

Equations notational: F_c = m v^2 / r; a_c = v^2 / r.

If the net force is toward the center, radial motion remains circular; any deviation results in a different trajectory. The concept emphasizes direction rather than a new kind of force.

In German physics literature, Zentripetalkraft is the standard term for centripetal force, and Zentripetalbeschleunigung for centripetal acceleration; the adjective zentripetal describes inward direction or related quantities. The idea is closely linked to the broader framework of Newtonian mechanics and is widely illustrated by everyday examples such as a car navigating a bend, a satellite in circular orbit around Earth, or a mass on a string swung in a circle.

Centripetal concepts are contrasted with centrifugal effects, which appear as outward forces in a rotating reference frame rather than as real forces acting on the object. In inertial frames, centripetal force is produced by real interactions that alter the direction of velocity.