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Newton's first law is part definition and part experimental. Isolated bodies move uniformly in inertial systems by virtue of the definition of an inertial system. In contrast, the assertion that inertial systems exist is a statement about the physical world.

According to me, the assertion in the last lines follows from the following statement:

It is always possible to find a coordinate system in which isolated bodies move uniformly.

Am I right to think that the assertion follows from the above statement?

Next, an isolated body is considered to be free of forces. A body, not isolated, but experiencing a net zero force also moves uniformly in inertial systems. I state the following:

It is always possible to find a coordinate system in which bodies experiencing a net zero force move uniformly.

While I think this makes better sense to me, I am still leaving some room for doubt. Could I be wrong in making the above statement?

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    $\begingroup$ Read this answer. You would be more than satisfied... physics.stackexchange.com/q/70186 $\endgroup$ – Abhinav Dhawan Nov 27 '17 at 7:46
  • $\begingroup$ @AbhinavDhawan Some great answers there. However, the discussion there was about isolated bodies or bodies that are not interacting with the rest of the universe. Here, I am considering a body that is interacting with two or more bodies in a way that produces no real acceleration in it. $\endgroup$ – R004 Nov 27 '17 at 8:33
  • $\begingroup$ The discussion there covers both of your cases. The second case is covered under the Second Law in the joshphysics answer, if you set the total force to zero. Besides, your formulation is misleading. It only provides for one frame while a frame of any isolated body is inertial. $\endgroup$ – safesphere Nov 27 '17 at 10:49
  • $\begingroup$ @safesphere "It only provides for one frame while a frame of any isolated body is inertial" Is it possible for you to elaborate on this? $\endgroup$ – R004 Nov 27 '17 at 11:39
  • $\begingroup$ You state, "It is always possible to find a coordinate system..." This formulation implies that at least one such a system (frame) must exist, but does not require or guarantee more than one. $\endgroup$ – safesphere Nov 27 '17 at 11:49
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Well, since everything is relative to another, there isn't any standard inertial reference frame. So, you first consider a particular frame to be inertial( generally everything is calculated w.r.t earth even though it's in circular motion, which means it's accelerating), and calculate everything else w.r.t it.

For your first part, an example would be, two cars accelerating in the same direction, when seen from car frame are moving uniformly or at rest, but w.r.t. to an outsider, they are being acted upon by a force. So, you can find a system where bodies move uniformly w.r.t one frame but not all.

The above example answers your second query as well, since net force on any car as seen from other is zero, but not to an outside observer.

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Object at rest or in uniform motion cannot be perceived without memory in perceiver person. Even with memory the concept of object at rest or uniform motion over time (say extending to more than one moment which is again say time between two successive eye winks) exists only in mind over that time. The world appearing outside the mind renews every moment like the frames of a cinema film projected on a screen. In mind that screen is consciousness akin to mental ether. Memory in mind creates time and 'no motion over time' as rest, or 'uniform motion' over time. The language of physics ignores the fact that there is no world outside the mind but that world appears to exist outside the mind AS IF it has continuous existence outside the mind. What is studied in physics is only the 'AS IF outside the mind'; it is the model of the world and cosmos appearing in the mind of the person (including the physicist). This fact has to be stated even at the risk of expulsion of this writer from the physics stack exchange.

The state of the world perceived in the mind alters in the very next moment but not in all respects, say mountains do not move and breath is ever moving. But most of what appears in the model of world and cosmos seem to conform to laws of physics and other natural sciences formulated by gifted persons. The laws are discovered in their mind. Newton and Einstein were two such gifted persons.

The three laws of motion formulated by Newton hold in segments (say coordinate system, isolated body at rest or in uniform motion, a single force or no force, which are imagined in segments of the model of the world and cosmos of physics. Physicists formulate laws only for segments of the model and this is indicated by the rider 'other things remaining the same'. In this sense the question with an answer which is under consideration is OK.

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  • $\begingroup$ I do not find this answer convincing. It's, in fact, frustrating to read. Where is this knowledge coming from? $\endgroup$ – R004 Nov 27 '17 at 15:53
  • $\begingroup$ @R004 from within his own mind, of course, as per the answer. $\endgroup$ – Asher Nov 27 '17 at 18:10

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