In the presence of angular velocity, there can exist a fictitious centrifugal force. This force is observed from a non-inertial reference frame.

Fictitious centrifugal forces are associated with centripetal acceleration due to rotation of an object about a point.

To illustrate this concept, consider a particle

The centripetal acceleration of the particle (

This acceleration is pointing towards the center

The friction force (

Thus,

where

Now, let’s say there is no friction on the turntable, so that force

Since Newton’s Second Law applies to an inertial reference frame, this means that the particle must have zero acceleration relative to ground (which serves as the inertial reference frame). Thus, relative to a (non-inertial) reference frame attached to the turntable (and moving with it), the particle must move outwards, away from the center

From the point of view of an observer sitting on the turntable (and moving with it), the fictitious centrifugal force is the apparent force that appears to be acting on the particle, pushing it radially outwards, away from the center

The figure below illustrates the outward radial motion of the particle.

Now, the particle will also move radially outwards relative to the turntable, if the friction force

An interesting problem related to this is problem # 7 in Physics Questions page.

It is worth mentioning that the velocity of the particle relative to the turntable gives rise to another fictitious force, known as the Coriolis-force. And if the turntable has angular acceleration, this gives rise to yet another fictitious force, known as the Euler force.

The reactive centrifugal force is defined as the reaction force to a centripetal force. A centripetal force is the force exerted on an object that is experiencing centripetal acceleration — this force points towards the center of rotation.

Using the turntable discussed previously as an example, the reactive centrifugal force is the reaction force to the centripetal force

This is the force acting on the particle as it revolves around on the turntable with centripetal acceleration

Therefore, the reactive centrifugal force is the force exerted

Unlike a fictitious force, the reactive centrifugal force is a

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