# Centrifugal force

The term centrifugal force is used for two different, if sometimes easy to confuse, concepts. The common meaning of centrifugal force is one of the fictitious forces that appears to act on an object when its motion is viewed from a rotating frame of reference. This "force" is actually inertia, which is not a force at all.

Another, less popular definition is that centrifugal force is the reaction force exerted by an object moving in a circular path upon the object that is causing its circular motion, according to Newton's Third Law. This force is actually centipetal force.

## Centripetal force

The force that maintains circular motion is called centripetal force. If no force is exerted on an object, it moves in a straight line at a constant speed. To make the object deviate from that straight path into in a circular one, a centripetal ("center seeking") force must be exerted at right angles to the object's velocity, directed toward the center of the circle. Since this causes a change in the direction of the object's velocity, the centripetal force causes a corresponding centripetal acceleration, also toward the center.

Main article: Centripetal force

## Examples

A classic example of these forces in action is a passenger riding in a car. The car is initially heading along a straight line but then swerves around a corner. If we keep track of the passenger's motion relative to the car, the passenger's body is apparently pushed towards the outer edge of the car. This is the result attributed to the centrifugal force, but it is called a fictitious force because it is not caused by an interaction with another object.

## Inertial frame of reference

When viewed from an inertial frame of reference, what is really happening is that the passenger's inertia resists any change of motion and keeps the passenger moving along the initial straight line of motion. From this point of view, the only reason that the passenger is pushed to the outside of the car is that the person is still travelling in a straight line, and the car has accelerated. Once the passenger hits the door of the car, the car is then able to apply the centripetal force on the passenger to accelerate him or her around the turn with the car. Friction between the seat of the car and the seat of the passenger's pants is also a component of the centripetal force, and at lower speeds, where passengers do not slide, friction accounts for all of it. In turn, the passenger also exerts a reaction force upon the door: according to the alternative definition, this would also be called a centrifugal force.

## Rotating frame of reference

Viewed from a frame of reference that co-rotates with the car, the passenger remains stationary. Because the centripetal force exerted by the door of the car still exists independently of the reference frame, it appears that Newton's second law has been broken: A net force acts on the passenger, yet he does not accelerate. Newton's second law indeed does not hold in rotating frames of reference, but it can still be used for calculations if we add a correction term, which takes the form of a force directed away from the center of rotation. This is the centrifugal force; it is minus the centripetal force and given by:

${\displaystyle F_{c}=-m\omega \times (\omega \times r)}$,

where ${\displaystyle \omega }$ is the vector angular velocity of the rotation and ${\displaystyle r}$ is a vector from an arbitrary point on the rotation axis to the body (with mass ${\displaystyle m}$) experiencing the centripetal force. See Fictitious force for a derivation.

The centrifugal force is a sufficient correction term in Newton's second law only if the body being considered is stationary in the rotating frame. For bodies that move with respect to the rotating frame it must be supplemented with the Coriolis force.

## Confusion over term

Confusion has emerged over the term centrifugal force because of these two quite different definitions. According to one definition, centrifugal force acts on the object and is a fictitious force, that only exists in rotating frames of reference. The other force that has been referred to as centrifugal force is the real reaction force exerted by the object. The two meanings are sometimes confused because the two kinds of centrifugal force have the same magnitude and direction.

For this reason, teachers of science in recent years have tended to de-emphasize the centrifugal force when teaching about circular motion, and instead emphasize the central role (quite literally) of the centripetal force, since it is the force responsible for maintaining circular motion and centripetal acceleration. It is usually highly recommended that students of elementary mechanics think about rotational physics using only inertial frames of reference, thus avoiding the need to think about centrifugal force.