When speaking of the laws of motion, Aristotle, Galileo, Newton and Einstein should each be considered as laying a step in the rising stairs of knowledge.
Galileo and Newton both showed that the Aristotelian commonsense observation that rest is the natural state for objects on Earth was wrong, and (philosophically) shifted towards uniform motion as a natural state of things. It was Newton -when studying motion- who, with his
first law, emphasized not the cause of motion but the
cause of changes of motion.
This cause is the
net force, F (i.e., the sum of all forces acting on a body) quantified in Newton's
second law of motion by equalling it to the rate of change of the body's momentum
p (velocity
v multiplied by mass m). As long as the body's mass doesn't change, the law can be written:
F = dp/dt = d(mv)/dt = m dv/dt = ma
Any change in the velocity vector -either in magnitude or direction or both- represents an acceleration (
a).
Newton's
third law of motion states that forces always come in
action-reaction pairs. The second and third laws together permit a consistent description of the motions of interacting objects.
It was Galileo's idea of inertia that resulted in what is called the principle of
Galilean relativity, which states that the laws of mechanics are valid in all frames of reference in uniform motion. Its ultimate meaning being that there is no way of using the laws of motion to answer the question "am I moving?", since with respect to the laws of motion, the question is meaningless; only
relative motion matters.
Einstein showed that our commonsense notions of space and time are not quite right, and in the process he was able to extend the principle of Galilean relativity to all of physics in his special theory of relativity.
As a result all equations of motion (including those of Newton) are really only approximately correct; they work well for our everyday experience, and even for spacecraft probing the solar system, but they break down when relative speeds approach the speed of light.
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