What is Pseudoforce?

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A force that feels like it exists but doesn’t. The classic example is centrifugal force, the outward force you feel when going in a circle or making a sharp turn, it doesn’t exist. When you drive around a sharp turn you are initially moving in a straight line, as you turn the car is now moving in a different direction but your body is still moving in a straight line and so the car/seatbelt has to exert a force towards the center of the circle to change your direction, that is centripetal force it is real. But you fell like you are being pulled outward because of your own inertia, there is no centrifugal force pulling you outward it is a psudoforce or fictitious force.

Imagine that you are in a car accelerating. You feel pushed into the back of the seat. Now if an outside observer look at the car they see that because you have inertia, in order to accelerate the car must put a force on your body. The back of the seat accelerates your body. The resulting force you feel comes for your body resisting a change in motion. Thats inertia.

From your reference frame inside the car, you feel this force on your body. Which means that this F=ma doesn’t work. There is a force acting on object without apparent acceleration. This acceleration is acceleration you measure inside your reference frame. In other words in order to keep something stationary you have to apply a force. This apparent force that pushes object towards the back of the car isn’t real. If you change your reference point to be an outside observer, you see the car accelerating and objects trying to remain still, until something forces them to accelerate.

Imagine it like this, you are in a spaceship floating in space. There is a ball in the ship. The ship accelerates and the ball moves towards the back of the ship. From an inertial reference frame the ball moves towards the back because nothing is making it move with the spaceship. It doesn’t move, its stays still, the ship moves. But inside the ship it looks as though there is a force pushing that ball to the back. Thats a fictitious force or pseudo force.

We can introduce pseudo forces to model the movement of objects inside an accelerated frame of reference. In this case if the ship accelerates with a0 the equation would look like this F=m×a+m×a0. So if inside the spaceship you see that nothing accelerates the ball you have F=m×0+m×a0, F=m×a0. That is the pseudo force, you model the accelerated frame of reference with fake forces. If you want to make that ball sit still from the ship’s point of view you must apply a force in the opposite direction so the sum of forces will be zero. 0=m×-a0+m×a0, 0=m(a0-a0). From this another way to look at it is that if there isn’t apparent acceleration you feel forces. F+m×a0=m×a. So when you got F+m×a0=m×0, F cannot be 0. It must be -a0×m. If you want no apparent acceleration you need a force.

Pseudo forces are required to model accelerated frames of reference. This example was about translation but there is rotation. In a rotating frame of reference there are 3 pseudo forces: centrifugal force, Coriolis force and Euler force.

F=m×a works in inertial reference frames for accelerated frames of reference this definition must be modified. And the things we add to it are pseudo forces.

The technical definition is: a pseudoforce is one that is not observed by all inertial observers. So what does that mean?:

Many people can watch a physical process and get different observations. With Einstein’s general relativity, even the order and timing of things may depend on the observer. However, there are many things that all _initial_ (that is: non-accelerating) observers can agree upon, such as causality (“which event caused which”, if at all).

One example is centripetal force, everyone moving at a constant rate could measure that a weight swung around on a rope does so because the rope pulls on it. But someone inside the weight experience the fictitious pseudo centrifugal force, which happens only because they are not inertial, they are constantly swung around.

Often even called a _fundamental_ force, the most important pseudoforce is actually Gravity! By our modern understanding of Gravity coming from bending space and time, something “influenced” by gravity actually flies straightforward, it’s just the underlying fabric of nature that makes this the way it is. And indeed, an astronaut on the ISS experiences no forces, they just freely and inertially move through space (and time)!

It’s a force that looks like a force and can be measured like a force, but doesn’t work like a force normally does. So for example, if you’re sitting inside an accelerating car, you get pushed back into the seats, so it feels like you’re pushing the car backwards. Now if you were to use this force and plug it into the formular of acceleration of the car, you would get a result that the car is slowly accelerating backwards.

Obviously, you can’t do that. In reality, the force you measure is the car pushing you forwards. It’s just that from your perspective, it’s the other way around, because you’re sitting inside an accelerating car. That is why it’s called a pseudoforce and not a force.