Centrifugal & Centripetal Forces

Centrifugal force

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Not to be confused with Centripetal force.

Look up centrifugal force inWiktionary, the free dictionary.

Centrifugal force (from Latin centrum "center" and fugere "to flee") represents the effects of inertiathat 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 non-inertial 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.

Fictitious centrifugal force

Main article: Centrifugal force (rotating reference frame)

Centrifugal force is often confused with centripetal force. Centrifugal force is most commonly introduced as a force associated with describing motion in a non-inertial 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.

Reactive centrifugal force

Main article: Reactive centrifugal force

A reactive centrifugal force is the reaction force to a centripetal force. A mass undergoing curved motion, such as circular motion, constantlyaccelerates 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 thereactive centrifugal force.^{[9][10][11][12][13][14][15][16][17]}

Fictitious vs. reactive force

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	Non-inertial 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

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Centripetal force

From Wikipedia, the free encyclopedia

Not to be confused with Centrifugal force.

Roller coaster cars are forced through a loop by the track applying a centripetal force on them. The reactive centrifugal force of the cars, associated with their inertia, holds them on the track.

Figure 1: A simple example corresponding to uniform circular motion. A ball is tethered to a rotational axis and is rotating counterclockwise around the specified path at a constant angular rate ω. The velocity of the ball is a vector tangential to the orbit, and is continuously changing direction, a change requiring a radially inward directed centripetal force. The centripetal force is provided by the tether, which is in a state of tension.

Centripetal force is a force that makes a body follow a curved path:it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path.^[1][2] The term centripetal forcecomes from the Latin words centrum ("center") and petere ("tend towards", "aim at"), signifying that the force is directed inward toward the center ofcurvature of the path. Isaac Newton's description was: "A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a center."^[3]

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