In an inertial frame of reference, there is no centrifugal force because it is a fictitious force that only manifests in rotating, non-inertial frames.

In physics, an inertial frame of reference is defined as one where Newton’s first law of motion holds true. This law states that an object will either remain at rest or continue to move at a constant velocity unless acted upon by an external force. In such frames, all observed forces are real and arise from physical interactions. Conversely, the centrifugal force is categorized as a fictitious or pseudo force; it does not emerge from any direct physical interaction between objects, but rather from the acceleration of the frame itself.

To illustrate this concept, consider the scenario of a ball attached to a string and being swung around in a circular path. For an observer positioned outside the circle (in an inertial frame), the only force acting on the ball is the tension in the string, which exerts an inward pull towards the center of the circle. This tension provides the necessary centripetal force for the ball’s circular motion. Importantly, there is no outward force acting on the ball that would push it away from the center.

In contrast, from the viewpoint of an observer who is moving with the ball (in a rotating, non-inertial frame), it seems as though there is an outward force acting to push the ball away from the center. This perceived force is referred to as the centrifugal force. It is crucial to note that this is not a real force; rather, it is an apparent effect arising from the observer’s rotation. The observer in the rotating frame must introduce this correction factor to account for the acceleration of their frame.

In conclusion, the centrifugal force is a fictitious force that is only relevant in rotating, non-inertial frames of reference. In an inertial frame, all forces are real and derive from physical interactions, eliminating the need for the concept of centrifugal force. This distinction explains why centrifugal force does not exist in inertial frames.