Centrifugal Force - Fictitious Centrifugal Force

Fictitious Centrifugal Force

Centrifugal force is often confused with centripetal force. Centrifugal force is most commonly introduced as an outward force apparent in a rotating frame of reference. It is apparent (fictitious) in the sense that it is not part of an interaction but is a result of rotation — with no reaction-force counterpart. This type of force is 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).

There are three contexts in which the concept of fictitious centrifugal force arises when describing motion using classical mechanics:

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 square of the rate of rotation (angular velocity) 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. 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.

The third context arises in Lagrangian mechanics, and refers to a subset of generalized forces that often are not equivalent to the vector forces of Newtonian mechanics. The generalized forces are called "generalized centrifugal forces" in this context (the word generalized is sometimes forgotten). They are related to the square of the rate of change of generalized coordinates (for example, polar coordinates), used in the Lagrangian formulation of mechanics. This topic is explored in more detail below.

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 are necessary for the formulation of correct equations of motion in a rotating reference frame.