Centrifugal force

The magnitude of the centrifugal force F on an object of mass m at the distance r from the axis of a rotating frame of reference with angular velocity ω is:

From 1659, the Neo-Latin term vi centrifuga ("centrifugal force") is attested in Christiaan Huygens' notes and letters.

In 1673, in Horologium Oscillatorium, Huygens writes (as translated by Richard J. Blackwell):[3] There is another kind of oscillation in addition to the one we have examined up to this point; namely, a motion in which a suspended weight is moved around through the circumference of a circle.

[...] I originally intended to publish here a lengthy description of these clocks, along with matters pertaining to circular motion and centrifugal force[a], as it might be called, a subject about which I have more to say than I am able to do at present.

The same year, Isaac Newton received Huygens work via Henry Oldenburg and replied "I pray you return [Mr. Huygens] my humble thanks [...] I am glad we can expect another discourse of the vis centrifuga, which speculation may prove of good use in natural philosophy and astronomy, as well as mechanics".

Around this time, the concept is also further evolved by Newton, Gottfried Wilhelm Leibniz, and Robert Hooke.

[citation needed] Centrifugal force has also played a role in debates in classical mechanics about detection of absolute motion.

Around 1883, Mach's principle was proposed where, instead of absolute rotation, the motion of the distant stars relative to the local inertial frame gives rise through some (hypothetical) physical law to the centrifugal force and other inertia effects.

Today's view is based upon the idea of an inertial frame of reference, which privileges observers for which the laws of physics take on their simplest form, and in particular, frames that do not use centrifugal forces in their equations of motion in order to describe motions correctly.

These fictitious forces are necessary for the formulation of correct equations of motion in a rotating reference frame[15][16] and allow Newton's laws to be used in their normal form in such a frame (with one exception: the fictitious forces do not obey Newton's third law: they have no equal and opposite counterparts).

[15] Newton's third law requires the counterparts to exist within the same frame of reference, hence centrifugal and centripetal force, which do not, are not action and reaction (as is sometimes erroneously contended).

A common experience that gives rise to the idea of a centrifugal force is encountered by passengers riding in a vehicle, such as a car, that is changing direction.

If the car enters a curve that bends to the left, the passenger experiences an apparent force that seems to be pulling them towards the right.

It is needed within the passengers' local frame of reference to explain their sudden tendency to start accelerating to the right relative to the car—a tendency which they must resist by applying a rightward force to the car (for instance, a frictional force against the seat) in order to remain in a fixed position inside.

[17] However, it would be apparent to a stationary observer watching from an overpass above that the frictional force exerted on the passenger by the seat is not being balanced; it constitutes a net force to the left, causing the passenger to accelerate toward the inside of the curve, as they must in order to keep moving with the car rather than proceeding in a straight line as they otherwise would.

[18] Similar effects are encountered in aeroplanes and roller coasters where the magnitude of the apparent force is often reported in "G's".

Because the rotation is slow, the fictitious forces it produces are often small, and in everyday situations can generally be neglected.

However, the object is moving in a circular path as the Earth rotates and therefore experiencing a centripetal acceleration.

This reduced restoring force in the spring is reflected on the scale as less weight — about 0.3% less at the equator than at the poles.

Newton's law of motion for a particle of mass m written in vector form is:

However, Newton's laws of motion apply only in the inertial frame and describe dynamics in terms of the absolute acceleration

, and unlike the Coriolis force in particular, it is independent of the motion of the particle in the rotating frame.

Within this view of physics, any other phenomenon that is usually attributed to centrifugal force can be used to identify absolute rotation.

For example, the oblateness of a sphere of freely flowing material is often explained in terms of centrifugal force.

The oblate spheroid shape reflects, following Clairaut's theorem, the balance between containment by gravitational attraction and dispersal by centrifugal force.

That the Earth is itself an oblate spheroid, bulging at the equator where the radial distance and hence the centrifugal force is larger, is taken as one of the evidences for its absolute rotation.

[31] The operations of numerous common rotating mechanical systems are most easily conceptualized in terms of centrifugal force.

While the majority of the scientific literature uses the term centrifugal force to refer to the particular fictitious force that arises in rotating frames, there are a few limited instances in the literature of the term applied to other distinct physical concepts.

[33][34] Within this formulation the motion is described in terms of generalized forces, using in place of Newton's laws the Euler–Lagrange equations.

[39] However, the Lagrangian use of "centrifugal force" in other, more general cases has only a limited connection to the Newtonian definition.