On Newton’s Three Laws (not yet done)
On Newton’s Three Laws*
Typically, the first exposure to physics of someone learning it for the first time will be on Newton’s Laws. This shouldn’t be frowned upon even though many go into physics to learn the new more modern theories. These laws however have an elegance to them and an appreciation of them goes a long way. Newton’s laws are still what engineers use to calculate motion. They are easily grasped and intuitively clear.
The three laws of motion are:
1.) Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by forces to change that state.
2.) Change of motion is proportional to the force and takes place in the direction of the straight line in which the force acts.
3.) To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed along the same straight line.
What is a body? Here we will say that a body is a material point, that is, a Euclidean point endowed with mass, everything else is a composition of many mass points. What it mass? Newton gave a circular meaning for the term. He said that mass is defined by the density multiplied by the volume of the body but density cannot be disconnected from the concept of mass. We will talk about mass shortly.
What is the content of the first law? Evidently it defines what the term force means. Intuitively, a force is a “push” or “pull.” These are however anthropomorphic in origin. The first law in other words says that, if a body is seen not to be in its natural state, it is acted on by forces.
The first law also determines what coordinate systems are allowable. It says that any coordinate system (think of an observer making experiments) that moves with constant velocity is allowable. It seems paradoxical that someone can make measurements and then proceed to calculate and use the laws of mechanics while moving uniformly but this is the way nature works and it has been verified. Of course, the first law can never be fully tested but using it as an assumption leads to no contradictions.
The second law seeks to define the relationship between mass (a dynamical concept) and kinematics (the geometry of motion). Why then was this not the first law? The concept of force is seen to have been used before it was actually operationally defined. Many people saw this illogical inconsistency of the three laws and therefore made adjustments. These are, however, made only to make the laws and definitions follow logically but almost everyone has these notions already intuitively clear that we can start anywhere.
Nevertheless, we can start forming the laws by starting with an experiment. Suppose two bodies far away from any others that we may approximately neglect their effects. Experiment shows that these two bodies will interact. Let us say gravitationally. We measure their accelerations and form,
-a1 / a2 = M2,1
It is seen that M2,1 is a constant.
*Not yet done.