Centrifugal force (from Latin centrum "center" and fugere "to flee") represents the effects of inertia that arise in connection with rotation and which are experienced as an outward force away from the center of rotation. In Newtonian mechanics, the term centrifugal force is used to refer to one of two distinct concepts: an inertial force (also called a "fictitious" force) observed in a noninertial reference frame or a reaction force corresponding to a centripetal force. The term is also sometimes used in Lagrangian mechanics to describe certain terms in the generalized force that depend on the choice of generalized coordinates.
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Centrifugal force is most commonly introduced as a force associated with describing motion in a noninertial reference frame, and referred to as a fictitious or inertial force (a description that must be understood as a technical usage of these words that means only that the force is not present in a stationary or inertial frame).^{[1]}^{[2]} There are three contexts in which the concept of the fictitious force arises when describing motion using classical mechanics.^{[3]} In the first context, the motion is described relative to a rotating reference frame about a fixed axis at the origin of the coordinate system. For observations made in the rotating frame, all objects appear to be under the influence of a radially outward force that is proportional to the distance from the axis of rotation and to the rate of rotation of the frame. The second context is similar, and describes the motion using an accelerated local reference frame attached to a moving body, for example, the frame of passengers in a car as it rounds a corner.^{[3]} In this case, rotation is again involved, this time about the center of curvature of the path of the moving body. In both these contexts, the centrifugal force is zero when the rate of rotation of the reference frame is zero, independent of the motions of objects in the frame.^{[4]}
The third context is related to the use of generalized coordinates as is done in the Lagrangian formulation of mechanics, discussed below. Here the term "centrifugal force" is an abbreviated substitute for "generalized centrifugal force", which in general has little connection with the Newtonian concept of centrifugal force.
If objects are seen as moving from a rotating frame, this movement results in another fictitious force, the Coriolis force; and if the rate of rotation of the frame is changing, a third fictitious force, the Euler force is experienced. Together, these three fictitious forces allow for the creation of correct equations of motion in a rotating reference frame.^{[4]}
A reactive centrifugal force is the reaction force to a centripetal force. A mass undergoing curved motion, such as circular motion, constantly accelerates toward the axis of rotation. This centripetal acceleration is provided by a centripetal force, which is exerted on the mass by some other object. In accordance with Newton's Third Law of Motion, the mass exerts an equal and opposite force on the object. This is the "real" or "reactive" centrifugal force: it is directed away from the center of rotation, and is exerted by the rotating mass on the object that originates the centripetal acceleration.^{[5]}^{[6]}^{[7]}
The concept of the reactive centrifugal force is used often in mechanical engineering sources that deal with internal stresses in rotating solid bodies.^{[8]} Newton's reactive centrifugal force still appears in some sources, and often is referred to as the centrifugal force rather than as the reactive centrifugal force.^{[9]}^{[10]}^{[11]}^{[12]}^{[13]}^{[14]}^{[15]}^{[16]}^{[17]}
The table below compares various facets of the "fictitious force" and "reactive force" concepts of centrifugal force
Fictitious centrifugal force  Reactive centrifugal force  

Reference frame 
Noninertial frames  Any 
Exerted by 
Acts as if emanating from the rotation axis, but no real source 
Bodies moving in circular paths 
Exerted upon 
All bodies, moving or not; if moving, Coriolis force also is present 
The object(s) causing the curved motion, not upon the body in curved motion 
Direction  Away from rotation axis, regardless of path of body 
Opposite to the centripetal force causing curved path 
Analysis  Kinetic: included as force in Newton's laws of motion 
Kinematic: related to centripetal force 
Lagrangian mechanics formulates mechanics in terms of generalized coordinates {q_{k}}, which can be as simple as the usual polar coordinates or a much more extensive list of variables.^{[18]}^{[19]} Within this formulation the motion is described in terms of generalized forces, using in place of Newton's laws the Euler–Lagrange equations. Among the generalized forces, those involving the square of the time derivatives {(dq_{k} / dt)^{2}} are sometimes called centrifugal forces.^{[20]}^{[21]}^{[22]}^{[23]}
The Lagrangian approach to polar coordinates that treats as generalized coordinates, as generalized velocities and as generalized accelerations, is outlined in another article, and found in many sources.^{[24]}^{[25]}^{[26]} For the particular case of singlebody motion found using the generalized coordinates in a central force, the Euler–Lagrange equations are the same equations found using Newton's second law in a corotating frame. For example, the radial equation is:
where U(r) is the central force potential. The left side is a "generalized force" and the first term on the right is the "generalized centrifugal force". However, the left side is not comparable to a Newtonian force, as it does not contain the complete radial acceleration, and likewise, therefore, the terms on the righthand side are "generalized forces" and cannot be interpreted as Newtonian forces.^{[27]}
The Lagrangian centrifugal force is derived without explicit use of a rotating frame of reference,^{[28]} but in the case of motion in a central potential the result is the same as the fictitious centrifugal force derived in a corotating frame.^{[3]} The Lagrangian use of "centrifugal force" in other, more general cases, however, has only a limited connection to the Newtonian definition.
The consideration of centrifugal force and absolute rotation is a topic of debate about relativity, cosmology, and the nature of physical laws.
Can absolute rotation be detected? In other words, can one decide whether an observed object is rotating or if it is you, the observer that is rotating? Newton suggested two experiments to resolve this problem. One is the effect of centrifugal force upon the shape of the surface of water rotating in a bucket. The second is the effect of centrifugal force upon the tension in a string joining two spheres rotating about their center of mass. A related third suggestion was that rotation of a sphere (such as a planet) could be detected from its shape (or "figure"), which is formed as a balance between containment by gravitational attraction and dispersal by centrifugal force.
The conception of centrifugal force has evolved since the time of Huygens, Newton, Leibniz, and Hooke who expressed early conceptions of it. The modern conception as a fictitious force or pseudo force due to a rotating reference frame as described above evolved in the eighteenth and nineteenth centuries.
The concept of centrifugal force in its more technical aspects introduces several additional topics:
The analogy between centrifugal force (sometimes used to create artificial gravity) and gravitational forces led to the equivalence principle of general relativity.^{[29]}^{[30]}
In physics, centrifugal force (from Latin centrum "center" and fugere "to flee") is a fictitious force that appears when describing physics in a rotating reference frame; it acts on anything with mass considered in such a frame. Centrifugal force is fictitious because although it may feel to a person like a certain force is being exerted on them, someone outside the scene will see something different.
Example: If John is in a car that takes a sharp right turn, he will feel as though he is being pushed to his left. This is an imaginary force, called a centrifugal force, or a "running away from the center" force. John feels it because he is inside the car and is affected by it. However, if John's friend, Andy, is on the side of the road facing the front of John's car and watches John's car take a sharp right turn, Andy will see the car push John to the right with the car as it changes direction. This is a real force called centripetal force (or an "aiming towards the center" force) and acts towards the center of the circle of rotation.
In other words, John's body, traveling in a straight line before the car turned, wanted to keep moving in a straight line because it had momentum in that direction, but the car, which was exerting a force on John by turning, is pulling him to the right. John feels like his body is being pushed to the left as the car turns, but in fact, his body is being pulled to the right by the turning car.
This is a problem that appears in rotating situations. There is a difference between what appears to be happening if watched from the outside or if the event was seen from within a rotating object. These differing viewpoints are called frames of reference.
Despite the name, fictitious forces are experienced as very real by anyone whose immediate environment is a noninertial frame. Even for observers in an inertial frame, fictitious forces provide a natural way to discuss dynamics within rotating environments such as planets, centrifuges, carousels, turning cars, and spinning buckets.
