# Newtons first law and inertial reference systems. (noob)

## Main Question or Discussion Point

Hi everyone,

Recently i started a self-study in classical physics by reading through some books. In the section that described Newton's first law I stumbled upon something that did not make much sense. The following section of text got me confused.

"If the net force acting on a body is zero, then it is possible to find a set of reference frames in which that body has no acceleration". (these frames are later referred to as inertial reference frames).

My problem started here. Let's assume for simplicity that our solar system is the only thing in the universe (also ignoring the rotation of the earth around its axis). There is a centripetal force that keeps objects rotating around the sun. Let's assume there is an object on earth with a net force of 0 exerted on it. This means that the centripetal force required to rotate around the sun is cancelled by other forces. This object will not rotate around the sun like the earth does, so it will accelerate and move relative to any reference frame on the earth. Therefore there can not be any inertial reference frame on the earth, since any object with net force = 0 will move relative to the earth!

Using the same reasoning, the solar system will also rotate around the centre of the Milky Way. Any object in the solar system with a net force of 0 will have its centripetal force for rotation around the centre of the milky-way cancelled. This object will accelerate and move relative to any reference frame in the solar system (because this reference system does rotate around the centre of the Milky Way).

The only real inertial reference system I can think of is one that does not move relative to the centre of the universe. But this is not really practical for applications on Earth. The book I'm using does use examples with inertial reference frames on Earth. For example a person observing a car hitting the brakes really hard (he sees the objects inside the car move without a change in velocity although the person inside the car seems to observe objects accelerate with no force exerted on them). But according to my reasoning before there can not be an inertial reference frame on Earth! Am I over-thinking right now or do I maybe misunderstand the concept of inertial reference frames? (or does this require relativity theory or something?) Thanks for reading this far! I hope you can give me a tip.

With kind regards,

Bremvil

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Yes, if you assume the center of the universe as an inertial system, then only systems moving with respect to it at constant velocity are inertial systems (Galileo's Relativity). This, of course, in the framework of newtonian mechanics. Every system that has acceleration respect the center of the universe is not inertial. However, if the acceleration is small compared to the typical acceleration of the body you are observing, then your system is quasi-inertial, and, for practical purposes, you can regard it as inertial. So, for example, you can take the Earth as inertial even if it rotates about itself, around the Sun, around the Milky Way, etc. Try calculating the centrifugal acceleration on the Earth's surface due to its rotation, or due to rotation around the Sun, and you will see that it is much smaller than 9.81 m/s^2. However, if your measurements are accurate enough, you can see the non inertiality of Earth, so, for example, you weigh more at the poles than on the equator.

Thanks :)! That clears it up for me. It would be nice if (introductory) physics books were more focusing on these details. Now it caused unnecessary confusion.

Well I guess you already got the answer, but clearing it up again for you,
"Earth is not an inertial system", so you are right about that. Almost all textbooks "mention this fact". I wonder how yours doesn't. All textbooks do mention the fact that earth is "approximately" an inertial frame, for practical purposes.

Since there is no "center of the universe", a better way to think about an actual inertial frame, is to say, a frame that does not interact with any other thing in the universe. The only way of interaction as far as we know are the four fundamental forces about which, I presume, you already know.
So a frame which doesn't interact with any other thing, will not feel any force on it, and thus "will not accelerate with respect to any other thing in the universe and nor will any other object accelerate with respect to this frame".

Cheers!!

Thanks for the help! It's much clearer for me now.