When an object travels in a circle it behaves as if it was experiencing an outward force which is known as the centrifugal force and depends on the mass of the object, the speed of rotation, and the distance from the center.

It is important to understand that the centrifugal force does not exist in reality and we only feel it because we are in a non-inertial coordinate system. Nevertheless, it appears quite real to the object being rotated. This is because the object believes that it is in a non-accelerating situation, when in fact it is not. Because the centrifugal force appears to be so real, it is often very useful to use as if it were real.

Centrifugal force is a term that refers to two different forces, which are related to rotation. From Latin the centrifugal force could be described as the force that helps the object to flee out of the circle. The two forces that Centrifugal force represents are both oriented away from the axis of rotation, but the object on which they are exerted differs.

**The reactive centrifugal force** is the reaction to the centripetal force, which is equal equal in magnitude to the centripetal force, directed away from the center of rotation. this force is exerted by the rotating object upon the object which exerts the centripetal force.

**The fictitious centrifugal force** appears when a rotating reference frame is used for analyzing the system. The centrifugal force is exerted on all objects in the frame, and directed away from the axis of rotation.

Both of the forces described above can be observed in action on a passenger riding in a car. When a car travels around a corner, the passenger's body pushes against the outer edge of the car. This is is an example of the reactive centrifugal force, which can also be called a reaction force because it results from passive interaction with the car which actively pushes against the body. When we use a reference frame which is fixed relative to the car and if we ignore its rotation, it looks like an external force is pulling the passenger out of the car. This is force is called the fictitious centrifugal force because it is not an actual force exerted by some other object.

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## Reaction centrifugal force[edit | edit source]

Centrifugal force serves as a reaction force to centripetal force, which is the force needed to move an object in a circle at constant speed. According to Newton's first law of motion, a moving body travels along a straight path with constant speed unless it is acted on by an outside force. For circular motion to occur there must be a constant force acting on a body, pushing it toward the center of the circular path. This force is called centripetal force. Centripetal force can exist in many different ways. For example the centripetal force for a planet orbiting the sun would be the gravitation force; for an object twirled on a string it would be mechanical force; for an electron orbiting an atom it would be electrical force. According to Newton's third law of motion, for every action there is an equal and opposite reaction. The centripetal force, the action, is balanced by a reaction force, the centrifugal force, which can also be described as center fleeing. These two forces are equal in magnitude and opposite in direction. While the centripetal force acts on the body in motion the centrifugal force acts on the source of the centripetal force to displace it radially from the center of the path. Therefore when we rotate a mass on a string, the centripetal force transmitted by the string pulls in on the mass to keep it in its circular path, while the centrifugal force transmitted by the string pulls outward on its point of attachment at the center of the path.

Centrifugal force can be explained on an example of car with passengers traveling through the curve. When we want to observe the reaction centrifugal force we have to view the situation from an inertial frame reference, which means from the passengers point of view. When the car travels through the curve the passenger's inertia resists acceleration, keeping the passenger moving with constant speed and direction as the car begins to turn. From this point of view, the passenger does not gravitate toward the outside of the car but the car curves to meet the passenger. Once the car contacts the passenger, it then applies a sideways force to accelerate him or her around the turn with the car. This force is called a centripetal force because its vector changes direction to continue to point toward the center of the car's arc as the car traverses it. Now we know that the car is acting upon the passenger and therefore the passenger must be acting upon the car with an equal and opposite force. We know that this reaction force have to be opposite to the centripetal force, which is directed to the center of the circular motion. Therefore this reaction force is directed away from the center and we call it centrifugal force. It is important to realize that this centrifugal force acts upon the car, not the passenger.

The centrifugal reaction force is given by a simple equation:

## Fictitious centrifugal force[edit | edit source]

The second force that that the Centrifugal force term refers to is a Fictitious centrifugal force. From the name of this force "fictitious" we know that this force doesn't really exist and we only pretend that it exist in reality. A fictitious centrifugal force is a force that acts on all masses in a rotating reference frame. This force does not arise from any physical interaction, but rather from the acceleration a of the non-inertial reference frame itself. This force must be included in the calculation of equilibrium between forces in a rotating reference frame. In the rotating frame, the forces on a body of mass m are in equilibrium only if all forces acting on it, plus a centrifugal force mv²/R directed away from the center of rotation, add up to zero. This is why the centripetal force is often referred to as "fictitious force." To achieve equilibrium we have to include the fictitious centrifugal force, which is assumed to be a reaction to the centripetal force needed to keep an object moving on a curved path, in our calculations.

Although it is not a real force according to Newton's laws and is often referred to be fictitious, the centrifugal-force concept is a useful one, because it helps explains the sensations a rider experiences while on a roller coaster. For example, when analyzing the experience of a vertical loop, it is convenient to study the rider's sensations relative to the looping coaster rather than relative to the Earth. In order that Newton's laws be applicable in such a rotating frame of reference, an inertial force, or a fictitious force (the centrifugal force), equal and opposite to the centripetal force, must be included in the equations of motion.

To describe the fictitious centrifugal force we use its **potential energy**. It is given by equation:

The potential energy of the centrifugal force is also used in the calculation of the height of the tides on the Earth where the centrifugal force must be included into calculations to account for the rotation of the Earth around the Earth-Moon center of mass.

## How to calculate Centrifugal Force?[edit | edit source]

We know that the centrifugal force is same in magnitude but opposite in direction to the centripetal force. Centripetal force acts to in the direction of the center of the circle and is given by equation:

**Fc = mv2/r**

where: Fc = centrifugal force m = mass v = speed and r = radius

The Centrifugal force act in an opposite direction of the Centripetal force but it has the same magnitude. Therefore the equation of the centrifugal force is given by equation:

**Fcentrifugal = -mv2/r**

## How to increase Centrifugal Force?[edit | edit source]

Centrifugal force can be increased by increasing either the speed of rotation, or the mass of the body that the force "acts on", or (3) the radius, which represents the distance of the body from the center of the curve. Increasing either the mass or the radius increases the centrifugal force proportionally. Increasing the speed of rotation increases it in proportion to the square of the speed what means that an increase in speed of 10 times increases the centrifugal force by a factor of 100. Centrifugal is expressed as a multiple of g, the symbol for normal gravitational force (strictly speaking, the acceleration due to gravity).

## References[edit | edit source]

Centrifugal Force: A "Fictitious" Force?