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As the merry-go-round rotates, the ball traces a circular path. String tension provides the centripetal force directed toward the center. By Newton's third law, an equal and opposite outward reaction force acts on the ball, called centrifugal force. This outward force pushes the ball away from the center of rotation.

Centrifugal force is a pseudo force, or fictitious force, that appears only in rotating, non-inertial reference frames. It is not a real force but a mathematical construct introduced to simplify calculations using Newton's laws in non-inertial frames. Centrifugal force does not obey Newton's third law because action and reaction forces must exist in the same reference frame.

In an inertial frame, only real forces like string tension (centripetal force) are needed to describe circular motion. In a rotating frame, centrifugal force must be introduced to balance the centripetal force, keeping the object stationary relative to that frame. This difference arises because the rotating frame is non-inertial and accelerating.

Centrifugal force equals the product of the object's mass, the square of its angular velocity, and its distance from the axis of rotation. This formula mirrors the centripetal force calculation but points outward instead of inward. The magnitude depends on how fast the object rotates and how far it is from the rotation axis.

Pseudo forces are necessary to formulate correct equations of motion using Newton's first and second laws in non-inertial frames. Without introducing centrifugal force in a rotating frame, Newton's laws appear violated because the object remains stationary despite an inward centripetal force. Adding the outward centrifugal force makes the net force zero, satisfying Newton's laws.

No, centrifugal and centripetal forces are not action-reaction pairs. Newton's third law requires that action and reaction forces exist in the same reference frame. Centripetal force acts in inertial frames, while centrifugal force exists only in rotating, non-inertial frames. They cannot be true action-reaction pairs because they operate in different reference frames.

Pseudo forces are essential in mechanics, astrophysics, and fluid dynamics, where motion in non-inertial reference frames is commonly encountered. Understanding centrifugal force helps explain phenomena in rotating systems like planetary motion, weather patterns, and rotating machinery. These fictitious forces simplify calculations in fields where rotating frames are the natural observation perspective.