This is a conceptual understanding of Newtonian mechanics. What the laws mean, how we know they're true, etc. I'm looking for criticism. I know this is really border line on the "don't ask questions that can't be answered" rule, but here we go anyway.
First Law: A body retains its velocity unless acted upon by an outside force.
This first law is actually a definition, not an empirical statement. Body can be defined based on sense data, as can be velocity. But force is as yet undefined. As it is the only undefined term in the statement, the statement must be a definition. A force is defined as "that which is said to 'act upon' a body when that body's velocity changes, the immediate cause for a change of velocity". This contrasts with the Aristotelian definition, which is "that which is said to 'act upon' a body when that body has non-zero velocity, the immediate cause for a change in position".
Second Law: A body's acceleration is a function of its mass and the force acting upon it, according to the relation F = ma.
This second one is still just a definition. It's implied that mass is a function of the specific body. We can apply this to predict accelerations (see Applications, below).
Third Law: When one body exerts a force on another, that other exerts an equal and opposite force on the first. This is the only of the three laws that is empirical. It is not a definition as force was already defined by the first two laws, and it cannot be proven logically from the first two. It would have to be proven by some sort of experiment.
The most glaring omission from the Laws is what can cause a force. Newton probably just meant it to be implied that forces were caused by collisions between bodies. In any case, you can demonstrate experimentally that collisions cause forces. This is the first apparent strength of Newtonian physics over Aristotelian physics. The Aristotelian definition of a force is valid (no such thing as a false definition), but in Newtonian mechanics it's much easier to express the relationship between collisions and forces.
We can apply these laws to calculate masses, forces, and accelerations.
- Define a unit mass. Mass is an unchanging property of a body and therefore we may simply take an arbitrary body and define its mass as the unit.
- Notice that when the same object collides with the same object in the same way, it has the same acceleration. For example, roll the same ball into it from the same height down the same slope, or hit it with a pendulum dropped from the same height. This provides inductive evidence that that sort of collision always produces the same force (F = ma, m is unchanging, a is unchanging, therefore F is unchanging).
- Now apply that collision to other objects to deduce their mass. If an object accelerates x times as much as the object of unit mass, it has 1/x mass.
- You can now measure mass.