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Newtons laws of motion:

1.An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.

2.The acceleration of an object depends on the mass of the object and the amount of force applied.

3.Whenever one object exerts a force on another object, the second object exerts an equal and opposite on the first.

What exactly did Newton do to prove his statements? Did he give a mathematical proof or was it experimentally based? Why did so many people accept that his statements will always hold true?

I am so sorry if my question offends you. It's just that I don't know much about the history.

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Let's leave aside the history of Mechanics and let's concentrate on the structure of any Physical law. Physics is about the real world. In practice, this statement means that at variance with Mathematics, we are not entitled to choose the starting point (axioms in mathematics) of any physical theory at our will.

The meaning of Principle in physics is that it is a statement directly or indirectly based on many experiments. Therefore, there is nothing like a mathematical proof. However, it is also not necessary that there direct experiments confirming the principles. It is enough that the consequences extracted from the principles agree with the experiments.

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  • $\begingroup$ Maybe I misread but this is not true. You could start with the coloumbs distance force or the E field. That is actually a choice. Or you can start with Lagrange formalism (LL, volume 1) instead of Newtons law. Any equivalent formulation can be used as a basis even in physics. $\endgroup$
    – lalala
    Dec 5, 2021 at 11:01
  • $\begingroup$ @lalala I think you misread. I wrote nowhere that there is a unique formulation of the principle of a physical theory. Certainly, there are many possible formulations of the principles, and in some way, they have not to be completely equivalent. However, the need of rooting any set of principles in the experimental data is unvoidable. $\endgroup$
    – GiorgioP
    Dec 5, 2021 at 21:46

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