Reactive centrifugal force

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${\displaystyle {\textbf {F}}={\frac {d}{dt}}(m{\textbf {v}})}$ Second law of motion
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In classical mechanics, a reactive centrifugal force forms part of an action–reaction pair with a centripetal force.

In accordance with Newton's first law of motion, an object moves in a straight line in the absence of a net force acting on the object. A curved path ensues when a force that is orthogonal to the object's motion acts on it; this force is often called a centripetal force, as it is directed toward the center of curvature of the path. Then in accordance with Newton's third law of motion, there will also be an equal and opposite force exerted by the object on some other object,^[1][2] and this reaction force is sometimes called a reactive centrifugal force, as it is directed in the opposite direction of the centripetal force.

In the case of a ball held in circular motion by a string, the centripetal force is the force exerted by the string on the ball. The reactive centrifugal force on the other hand is the force the ball exerts on the string, placing it under tension.

Unlike the inertial force known as centrifugal force, which exists only in the rotating frame of reference, the reactive force is a real Newtonian force that is observed in any reference frame. The two forces will only have the same magnitude in the special cases where circular motion arises and where the axis of rotation is the origin of the rotating frame of reference.^[3][4][5][6]