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It is often questioned by people who have begun learning physics why the 1st Law of Newton is necessary, since the 2nd Law seems to imply it anyways. A modern interpretation of the first law that clarifies why the 1st Law is not redundant, as one might suspect, is that in essence the 1st Law asserts the existence of at least one frame of reference (and thus, infinitely many based on that) with respect to which a body in space, devoid of a non-zero net force acting on it, "truly" does not experience acceleration. The relation between mass, acceleration and net force put forward by the 2nd Law only holds w.r.t. a frame of reference as postulated by the 1st Law, without which the statement would have no actual value.

The reason why I included "truly" in my explanation is that whether we decide a body has acceleration or not is on a fundamental level totally arbitrary: there is no actual justification of concluding that a car hitting the breakes on the road is the body that is accelerating and us watching from outside are the ones stagnant: An observer from within the car could well argue that he is the one who is not accelerating (which would be a true statement w.r.t. an origin of reference, say the guy sitting in the car himself) and instead the observers from outside the car are the ones accelerating w.r.t. his frame of reference.

Again, there is no justification of calling the so called effects of inertia as "fictitious forces w.r.t. a non-inertial frame of reference". Deciding which changes in acceleration are due to a "real force" and which are due to "fictitious forces" therefore, appears to be arbitrary.

The purpose the 1st Law serves here is that it provides that justification: It asserts that with respect to a "true" frame of reference (i.e., an inertial one) the 2nd Law holds and forces that "truly exist" are defined in terms of such frames of reference.

Is my understanding correct? Are there any major points which I am misunderstanding/misinterpreting?

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  • $\begingroup$ No, no need for the "truly" word,- frames which experiences acceleration becomes non-inertial ones and these which don't - inertial frames of reference. You can differentiate between those two by the fact that non-inertial frames experiences pseudo-forces and inertial ones - don't. Car passengers will feel "forwards pushing" force upon braking, while observers outside - will not feel such pseudo force and hence,- those frames are not equivalent. One inertial and second - non-inertial. $\endgroup$
    – Agnius Vasiliauskas
    Commented Oct 26 at 12:15
  • $\begingroup$ @AgniusVasiliauskas how does one differentiate between a pseudo-force and a real force? How do we know that the push forward experienced by the person sitting in the car is not a real force? $\endgroup$
    – David06
    Commented Oct 26 at 12:19
  • $\begingroup$ Simply, in a decelerating frame, there's no any physical reason for new forces to arrive. This pseudo-force for passengers is just a manifestation of first Newton law,- bodies in the car tries to maintain same speed wrt outer (Earth) reference frame. All physical forces has real root causes, which pseudo forces - don't, that's why they are called "pseudo". On the other hand, if you put equal sign between inertial and non-inertial frames of references then first Newton law doesn't make sense to you, because it is specifically designed to differentiate between these cases, which you ignore. $\endgroup$
    – Agnius Vasiliauskas
    Commented Oct 26 at 12:30
  • $\begingroup$ I think I understand what you're saying. But again, the reason why we conclude that the push forward experienced within the car does not have a "physical cause" whereas other forces, e.g. gravitational force between objects do has to do with our empirical understanding of the universe, rather than a mathematical neccessity, which makes the existence of inertial frames ultimately a postulate as suggested by the 1st Law. $\endgroup$
    – David06
    Commented Oct 26 at 12:37
  • $\begingroup$ @David06 Gravity is precisely what demonstrates Agnius's point in fact. Einstein has shown that it is indeed correct to see it as a fictitious force. Nothing is pushing us towards the center of the earth, it is in fact (local) inertial motion in curved spacetime that causes us to tend to the center of the earth, while the ground beneath our feet is resisting that motion. Incidentally, gravity like other pseudo-forces is proportional to mass. This is another property that uniquely characterizes fictitious forces: since they are just a consequence of inertia, and inertia is proportional to mass $\endgroup$
    – Amit
    Commented Oct 26 at 18:38

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Whether embodied in a modern formulation of the first law or stated differently, inertial reference frames are essential in Classical Mechanics to allow the usual introduction of forces and their properties.

Indeed, the primary role of inertial frames is to eliminate the reference frame as the origin of the body's acceleration. In this way, acceleration originates only from interactions among bodies, and every force belongs to an action-reaction set of forces.

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There is an important difference between the braking car and the rest of the world. Newton's second law applies to the braking car, and can be consistently applied to other circumstances in which a massive body changes velocity. You cannot apply Netwon's law, or come up with anything as simple as it, if you take the car to be not accelerating and the rest of the world to be accelerating instead.

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