Centrifugal force

Centrifugal force is the outward force on a body moving in a curved path around another body.

Centrifugal force is directed outwards the centre of rotation
Centrifugal force is directed outwards the centre of rotation

Centrifugal force(from Latin centrum, meaning “centre”, andfugere, meaning “to flee“) is the apparent force that draws a rotating body away from the centre of rotation. It is caused by the inertia of the body as the body’s path is continually redirected.

This Centrifugal force represents two types of forces which are both oriented away from the axis of rotation, but differ in terms of the object on which they are exerted.

The fictitious centrifugal force

It appears when a rotating reference frame is used for analysing the system. It is exerted on all objects in the frame, and directed away from the axis of rotation.

To illustrate this concept, consider a particlePthat is firmly sitting on a turntable, which is rotating about pointOat angular velocityω. The radius measured from pointOto the location of the particle isR.

The fictitious centrifugal force
The fictitious centrifugal force

The centripetal acceleration of the particle (ac) with respect to ground is: ac = ω2r

This acceleration is pointing towards the centreOof rotation.

The friction force (Ff) between the particle and turntable is holding the particle in place. This force is determined by applying Newton’s Second Law in the direction ofac.

Thus, Ff = mac. = m(ω2r)

wheremis the mass of the particle.

The reactive centrifugal force

This is the reaction to the centripetal force, which is equal in magnitude to the centripetal force, directed away from the centre of rotation. This force is exerted by the rotating object upon the object which exerts the centripetal force.

The reactive centrifugal force (Fr )is given by Fr= m(ω2r)

This is the force acting on the particle as it revolves around on the turntable with centripetal acceleration (relative to ground).

Therefore, the reactive centrifugal force is the force exertedbythe particle onthe turntable. By Newton’s Third Law this force is acting in the direction opposite to the forceFc (centripetal force). This is illustrated in the figure below.

The reactive centrifugal force
The reactive centrifugal force

Unlike a fictitious force, the reactive centrifugal force is areal force based on the acceleration of the particle relative to an inertial reference frame (ground), which is given by ar = ω2r

Both of the forces described above can be observed in action on a passenger sitting in a car. When a car travels around a corner, the passenger’s body pushes against the outer edge of the car. This 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.