Some processes and phenomena that constantly accompany us, about the nature and causes of which we don’t even think about, upon deeper consideration, can be an inexhaustible source of information about the laws and rules that the whole physical world obeys.
It would seem that what is in common between an object resting in place and making a rectilinear uniform motion? The laws of motion were still interested in ancient thinkers. The "physics" of Aristotle, dating from the 4th century BC, contains the conclusions of the ancient Greek thinker about the nature of rest and movement. Practically following the right path in an attempt to explain this mundane phenomenon, he makes a very interesting conclusion in his next work, "Mechanics." Aristotle completely abandoned the use of the concept of "absolute emptiness" and concluded that for any movement, a constant effect on the object of a certain force is necessary. It indicates that with the cessation of the effect of force, motion also ceases. Thus, the thinker, being one step away from describing the law of inertia, followed the wrong path.
It took two thousand years of human thought to cast doubt on Aristotle's conclusions. The Italian physicist and philosopher, mechanic and astronomer Galileo Galilei found flaws in the interpretation of the nature of motion accepted by official science of that time. Galileo’s law of inertia is almost completely consistent with the modern explanation, but its remarkableness lies in the fact that it was impossible to use an experimental base for its formulation and proof due to the lack of ideal conditions. The Italian thinker made this conclusion on the basis of personal observations, by following from the contrary and using the method of exclusion.
Thus, the law of inertia is practically the brainchild of Galileo, although it is used by modern science in the Cartesian interpretation. Another merit of the great Italian is an indication that free movement is possible not only in a straight line, but also in a circle. In practice, it was precisely this assumption that made it possible to describe the rotational motion by inertia. The law of conservation of moment of inertia was a logical continuation of Galileo's conclusions.
Subsequently, the Englishman Isaac Newton created a whole system of laws of mechanics. He included the law of inertia in this system as the first. But science does not stand still - during the existence of the Newtonian system, it has been repeatedly criticized and attempts to revise the postulates contained in it.
The twentieth century, which became the period of a radical revision of traditional laws under the influence of Einstein's discoveries, introduced certain amendments to the interpretation of the basic laws of mechanics. But for practical use, engineering calculations and design of mechanical systems, conclusions and formulas of traditional mechanics are still applied.
When we use the law of inertia in practice, we have to make a number of assumptions when making calculations. It is almost impossible to achieve the existence of a full-fledged inertial system. When calculating, it is often easier to accept the system as non-inertial, which makes it impossible to use Newton's laws. Considering some unit relative to the reference system for which we take the car itself, we can use the law of inertia as long as the car stands still, or moves uniformly. During acceleration and braking, this reference system completely loses its inertial properties.
You can give a lot of examples when in order to obtain a result in simpler ways, factors are missed, although they are significant, but do not significantly affect the final conclusions. Modern mechanics fully admits such liberties, although for more accurate calculations it requires taking into account some factors by introducing various coefficients and corrections.