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The centripetal force is the external force required to make a body follow a curved path. Hence centripetal force is a force requirement, not a particular kind of force, like gravity or electromagnetic force. Newton's description is found in the Principia.
Any force (gravitational, electromagnetic, etc.) (or combination of forces) can act to provide a centripetal force. An example for the case of uniform circular motion is shown in Figure 1.
Centripetal force is directed inward, toward the center of curvature of the path Centripetal force should not be confused with centrifugal force. Centripetal force is a kinematic force requirement deduced from an observed trajectory, not a kinetic force like gravity or electrical forces. Centripetal force requirements may be deduced from a trajectory in any frame of reference (although the trajectory of an object and the deduced centripetal force will vary from one frame to another). Because centripetal force is a kinematic force requirement inferred from an established trajectory, it is not used to deduce a trajectory from a physical situation, and centripetal force is not included in the inventory of forces that are used in applying Newton's laws F = m a to calculate a trajectory.
Centrifugal force, on the other hand, is treated in a rotating frame as a kinetic force, that is, as part of the inventory of forces used in Newton's laws to predict motion. Centrifugal force is a fictitious force, however, that arises only when motion is described or experienced in a rotating reference frame, and it does not exist in an inertial frame of reference.
In classical mechanics, centrifugal force (from Latin centrum "center" and fugere "to flee") is an apparent force acting outward from the axis of a rotating reference frame. Centrifugal force is a fictitious force(also known as a pseudo force, inertial force or d'Alembert force) meaning that it is an artifact of acceleration of a reference frame. Unlike real forces such as gravitational or electromagnetic forces, fictitious forces do not originate from physical interactions between objects, and they do not appear in Newton's laws of motion for an inertial frame of reference; in an inertial frame, the motion of an object is explained by the real impressed forces. In a non-inertial frame, however, fictitious forces must be included along with the real forces in order to make accurate physical predictions. The fictitious forces present in a rotating reference frame with a uniform angular velocity are the centrifugal force and the Coriolis force, to which is added the Euler force when angular velocity is time dependent.
The centrifugal and Coriolis forces are called fictitious because they do not appear in an inertial frame of reference. Despite the name, fictitious forces are experienced as very real to those actually in a non-inertial frame. Fictitious forces also provide a convenient way to discuss dynamics within rotating environments, and can simplify explanations and mathematics.
An interesting exploration of the reality of centrifugal force is provided by artificial gravity introduced into a space station by rotation. Such a form of gravity does have things in common with ordinary gravity. For example, playing catch, the ball must be thrown upward to counteract "gravity". Cream will rise to the top of milk (if it is not homogenized). There are differences from ordinary gravity: one is the rapid change in "gravity" with distance from the center of rotation, which would be very noticeable unless the space station were very large. More disconcerting is the associated Coriolis force. These differences between artificial and real gravity can affect human health, and are a subject of study. In any event, the "fictitious" forces in this habitat would seem perfectly real to those living in the station. Although they could readily do experiments that would reveal the space station was rotating, inhabitants would find description of daily life remained more natural in terms of fictitious forces.
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