Fictitious force

A fictitious force, also called a pseudo force,d'Alembert force or inertial force, is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference, such as a rotating reference frame.

The force F does not arise from any physical interaction between two objects, but rather from the acceleration a of the non-inertial reference frame itself. As stated by Iro:

Such an additional force due to nonuniform relative motion of two reference frames is called a pseudo-force.

Assuming Newton's second law in the form F = ma, fictitious forces are always proportional to the mass m.

A fictitious force on an object arises when the frame of reference used to describe the object's motion is accelerating compared to a non-accelerating frame. As a frame can accelerate in any arbitrary way, so can fictitious forces be as arbitrary (but only in direct response to the acceleration of the frame). However, four fictitious forces are defined for frames accelerated in commonly occurring ways: one caused by any relative acceleration of the origin in a straight line (rectilinear acceleration); two involving rotation: centrifugal force and Coriolis force; and a fourth, called the Euler force, caused by a variable rate of rotation, should that occur. Gravitational force would also be a fictitious force based upon a field model in which particles distort spacetime due to their mass.

The role of fictitious forces in Newtonian mechanics is described by Tonnelat:

For Newton, the appearance of acceleration always indicates the existence of absolute motion – absolute motion of matter where real forces are concerned; absolute motion of the reference system, where so-called fictitious forces, such as inertial forces or those of Coriolis, are concerned.

The surface of the Earth is a rotating reference frame. To solve classical mechanics problems exactly in an Earth-bound reference frame, three fictitious forces must be introduced, the Coriolis force, the centrifugal force (described below) and the Euler force. The Euler force is typically ignored because the variations in the angular velocity of the rotating Earth surface are usually insignificant. Both of the other fictitious forces are weak compared to most typical forces in everyday life, but they can be detected under careful conditions. For example, Léon Foucault was able to show that the Coriolis force results from the Earth's rotation using the Foucault pendulum. If the Earth were to rotate a thousand times faster (making each day only ≈86 seconds long), people could easily get the impression that such fictitious forces are pulling on them, as on a spinning carousel.

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