Is the centrifugal force real?
The centrifugal “force” is a pseudoforce, or apparent force. It is not a true force because nothing pulls outwardly on you; it only feels like it. The law of inertia states that a body resists motion. In other words, a body at rest will stay at rest until acted upon by an external force and a body in motion will remain in motion unless acted upon by an external force. Your body is resisting the centripetal force keeping you from flying off the merry-go-round.
One situation you are likely familiar with is feeling pushed against the side of a car during a sharp turn. We can see that there is a force pulling on the car towards the center of a hypothetical circle. This circle has the same radius as that of the turn. Any physical body with mass, including yours, will resist moving toward the center. In the case shown with the car turning left, your body will feel like it’s being pulled out toward the right side. Remember, this is not a real force, but is a result of your body’s resistance to the real centripetal force acting on the car.
If there is any doubt as to calling centrifugal force apparent, ask yourself this: is anything directly pushing or pulling you? The answer is no, and should lead you to understand that this effect is, in fact, apparent.
Another way to look at this is through the use of an inertial frame of reference (IFOR). A frame of reference (FOR) is a system through which we can make observations. A set of coordinates is an example of an FOR. What makes one inertial is that the FOR is either moving at a constant velocity (not accelerating) or is not moving at all relative to the observed system.
As a passenger in a car, you perceive yourself to be the IFOR since it feels like you are at rest; from this perspective it appears that a force is applied on you. However, you are not an IFOR because you are accelerating centripetally with the car. Taking a stationary top down view, we can see that your body is not at rest and is moving with the car. If you take a snapshot of the car’s motion, say, when it is moving forward right before the turn, we will have motion in one direction at one speed. When the car starts turning, your body still want to move in this same direction and speed. The car will have to push on your body in the same direction as the centripetal force. While your body wants to keep moving straight forward, the car will push you sideways (towards the center of the circle). From your perspective, it feels like something is pulling you out of the car.