equilibrium position | lab frame | mass's frame

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In an inertial reference frame, momentum and energy are conserved even though observers may disagree on total momentum or total energy. As a consequence, if two observers were in inertial reference frames, the two observers would agree on the forces acting. Restart.

Consider a green mass at the end of a spring (position is shown in meters and time is shown in seconds). If the mass is not moving, the net force on it is zero, and therefore the gray shell represents the equilibrium position of the spring.

Now imagine that someone has given the green ball a brief push making it rotate with a constant speed as seen in the laboratory frame. We know that the spring must be stretched as shown. Why? Well, we need a force toward the center of the circle because this force is necessary for uniform circular motion. This force is the spring force.

Imagine you (the woman in the animation) are riding on the green mass. From your point of view, mass's reference frame, what is the motion of the green ball? It is stationary. In this reference frame the ball does not move. It is not, however, an inertial reference frame because it is accelerating. What happens to the spring in this frame? The spring is stretched from its equilibrium position as before. How would you explain this? From your point of view riding with the rotating mass, since you are not accelerating, the net force on the green ball is zero, and someone or something has stretched the spring by pulling it outward. This force is purely a figment of your imagination. This fictitious force—also called the centrifugal force (no more real because it has a name!)—must be invented by an observer on the green ball if she is going to keep Newton's laws as a fact of Nature. Whenever you are in a rotating reference frame, like a merry-go-round, for example, you are in an accelerating reference frame, and therefore you must invent fictitious forces to make Nature obey Newton's laws.