Is the centrifugal force a real force?

Suppose you are at a red light in your car. You apply Newton's second law on the street light. $$F=ma$$ $$F=0N, a=0ms^{-2}$$$$0N=0N$$

It works!!

Now the light turns green and you start accelerating. Suppose your acceleration is $1ms^{-2}$. According to you, you are at rest. Do you see your nose moving? Apparently not. It means your body is at rest wrt you. So street light has acceleration $-1ms^{-2}$ wrt you. Let's apply Newton's second law.


Clearly, there is no force acting on it. And the light,say, has mass=$50kg$



Your mind just blew, right? You see that you are unable to apply Newton's second law in an accelerating frame. Let's see how can we fix it.

IF we add $-50N$ on $LHS$ we will get the correct answer.

Hence, we define pseudo force as a correction term which enables us to apply Newton's second law in accelerating frames. It has no real existence, it is just a mathematical force.

Similarly, a centripetal force is needed to make you go in a circle. If you sit there, you have to apply a force outwards which we call centrifugal force, to use Newton's laws.

Centripetal force is a force which provides acceleration towards centre, say, Tension while moving the object round with string. So if, you apply $F=ma$ from the revolving object, you have to add centrifugal force as the object is at rest wrt itself.

You can explain what you experience while turning due to you inertia which resists you change in motion.

The force you feel when you round a corner in your car is the friction force of the car seat on your behind, and perhaps the pushing force of the door on your shoulder. These are very real forces that occur when your car tries to turn while your body tries to continue moving in a straight line.

But from your point of view in the car, with the windows painted black (!), you perceive yourself being thrust toward the door for no apparent reason. You feel as if there is a force acting on you, and the friction on your pants and the compression of your shoulder are a result of this force as you try to accelerate in the direction of that perceived force.

Since your car windows are painted black, the only frame of reference you know about is the one attached to the car, so you (quickly, because you are about to crash) reformulate mechanics to account for your observations. You see yourself being accelerated toward the door, so you have no choice but to associate a force with that acceleration. You call it "centrifugal", and you write it all down ... quickly.

A pseudoforce, like centrifugal force, the Coriolis force, or gravity, is a correction term we use in order to be able to apply standard physical models to accelerating reference frames, when the alternatives (rotational motion, rotation in 3-space, or relatativity) are conceptually or computationally harder to deal with.

Imagine the following problem setup:

A stack of concrete drainage pipes are loaded onto a flatbed truck. The truck takes a sharp banked turn, during which the straps holding the pipes come loose. Compute the motion of the pipes.

Now, one could solve this problem using relativity and rotational motion in three-dimensional space, or one could instead enlist pseudoforces to vastly simplify the problem, allowing us to deal with it using only 2D kinematics. Which sounds easier to you?