Why Do So Many People on Quora Believe That Centripetal Force Is Cancelled by Centrifugal Force?

From a layman's perspective, for an object to remain in a steady state of motion, its movement needs to be balanced by counteracting forces. This belief often leads to a common misconception that centripetal force, responsible for an object moving in a circle, is canceled by a fictitious centrifugal force. Such a belief overlooks the fundamental principles of physics, particularly in rotational motion. Let’s delve into this topic further.

The True Nature of Rotational Motion

Rotational motion is the movement of an object around a central point, and the central force maintaining this motion is the centripetal force. This force causes the object to move towards the center, keeping it in circular path. The centripetal force is real, as it results from the attractive force between two bodies, such as the gravitational pull of a planet on one of its moons or the tension in a string holding a mass in circular motion.

The belief that centripetal and centrifugal forces cancel each other stems from a misunderstanding of inertial forces. Centrifugal force is a fictitious force felt in a rotating frame of reference. It appears to push the object outward, away from the center, but it does not exist in an inertial (non-accelerating) frame of reference. In a rotating frame, the centrifugal force appears to balance the centripetal force, giving the false impression of cancellation. However, in an inertial frame, the centripetal force alone dictates the path of the object.

Understanding Centrifugal Force

Centrifugal force is often regarded as the inertial force caused by the mass of the revolving object. For example, when a car turns left, passengers feel as though they are pushed to the right. This sensation is not due to a force but a result of the car’s acceleration and the passengers' inertia. In the rotating frame of reference, the centrifugal force acts as a centripetal force would appear to counter the direction of motion, but in reality, it only affects objects in the rotating frame.

From the perspective of a mass connected by a string to a fixed point, the tension in the string provides the centripetal force, and the object experiences a centrifugal force in the rotating frame. These two forces are not physical forces cancelling each other; rather, they are perceived differently based on the frame of reference.

The Analysis of Circular Motion

To understand rotational motion, it is helpful to analyze the problem in a rotating reference frame. In this frame, the centripetal and centrifugal forces are often mentioned and treated as physical forces cancelling each other. However, this is a simplification that works only within the rotating frame. If one shifts the analysis back to an inertial frame, the centrifugal force ceases to exist, and only the centripetal force is needed to describe the circular motion.

Angular velocity, a measure of rotational speed, remains constant in both linear and circular reference frames. Linear velocity, on the other hand, varies as the object moves closer to or farther from the center. The kinematic equations for circular motion, such as those for acceleration and force, must account for the centripetal force. This force is the real force that keeps the object in its circular path.

By using a fictitious centrifugal force in the rotating frame to simplify calculations, the apparent cancellation of forces can be understood. However, it is crucial to realize that this cancellation is not a physical event but a simplification used for easier problem-solving. Outside this rotating frame, the central forces (centripetal force) are the only forces acting, and no centrifugal force exists.

Conclusion

The widespread belief that centripetal and centrifugal forces cancel each other on Quora arises from the confusion between real forces and fictitious forces. While centrifugal force is only perceived in a rotating frame, centripetal force is a real and necessary force for objects to move in a circular path. Understanding the distinction between these forces is key to grasping the dynamics of rotational motion. As in the case of analyzing a rotating system, the key is to recognize the correct frame of reference to interpret the forces acting on the object.