Really understanding Newtonian mechanics

Question

I absolutely abhor the way in which physics is taught at school. All they really do is prepare you for doing physics problems, making little effort to impart an actual understanding of the subject matter. I want to feel like I myself could have come up with the laws of physics from physical observations, and none of the lectures I've attended or the books I've read make a real attempt to do this. At most, there's an allusion in a footnote somewhere to how Newton found the laws using the results of Gallileo's prior experiments, never delving into specifics. I went so far as to try reading a translation of the original Principia, but I found that that too only states findings, not a word of how exactly they were derived/determined.

Are there any resources/books (on classical physics) that have what I'm looking for?

Answer 1

Chapter 1.2 & 1.3 of John Michael Finn's Classical Mechanics might contain what you are seeking.

Chapter 2 of Kleppner & Kolenkow's Introduction to Mechanics gives a good account of Newton's laws and how they can be 'deduced' empirically.

Answer 2

Newton's laws were derived by physical intuition and experimentation. I'm not sure how Newton derived them. Since you asked for thought experiments: imagine you kick a moving point football what all would you need to know predict the outcome? The below is a heuristic argument (and under scrutiny this is modelled by impulse but suffices to make the point).

I imagine one would need the velocity and position of the ball when it was kicked and position of the ball. This is already suggestive of second order differential equation (since there are $2$ unknowns). The direction of your kick is the same as direction of the "change" in motion.

So you apply a "kick" on a point ball $A$ and you see behave one way but you can imagine applying a "kick" on a heavier ball it's motion would behave differently. This "heaviness" is characterized by a parameter $m$ known as mass.

Putting this together:

$$\vec F = m \vec a$$

References: Griener Classical Theoretical Physics

Answer 3

You raise an interesting question:

Is is possible at all for teacher of physics to present the subject in such a way that the student comes close to feeling a process of personally discovering the laws of motion.

It seems to me the teaching must then start with demonstrations of motion and bounces by objects moving along an air track.

Also, the teaching must then make it plausible that objects, when released to free motion, proceed in a straight line. On the air track the track already constrains the motion to a straight line, so to make the free-motion-will-go-straight concept plausible the teaching equipment must include a large enough air table.

With bouncing demonstrations the conept of conservation of momentum can be made plausible.

Then the big one: make it plausible that acceleration is proportional to impressed force.

For that you need to provide a constant force, but that is tricky.
Let's say you put a glider on the air track, and you start pulling it with a length of string. How do you maintain a constant tension of the string as the glider is accelerating? (Use a setup with a pulley and a descending weight? Then you are assuming that such a setup maintains a constant tension.)

It is actually surprisingly hard to create circumstances such that you get an unobstructed view of $F=ma$ in action.

I remember reading the following story: one scholar had built a device that would eject marbles horizontally at a consistent velocity (consistent enough for his purpose). If acceleration due to gravity is uniform then the trajectory will be along a parabola.

The marbles fell alongside a board. Over the course of many throws he hammered nails in the board to the left and the right of the trajectory, all the way along the trajectory. That way he confirmed that the trajectory was consistent with gravity causing uniform acceleration.

I think at the time that was as close as you could get to $F=ma$

My point is: there are always things that are preventing direct observation of the underlying law.

Incidentally, for Newton and his contemporaries the task was much harder. Back then there were precursors of the modern concepts of force and momentum, but those concepts were still very much in flux.

Force was generally thought of as something that was transferred into an object, and in motion that force was then an internal force, sustaining the motion.

Source:
webpage by Micheal Fowler on Newton's development from pre-newtonian thinking to something closer to the modern concepts.

So back then the proces of discovering laws of motion wasn't just discovering laws of motion, it was just as much a discovery process of how to conceptualize the world such that you are able to formulate a theory of motion.

Answer 4

You might find 3blue1brown videos interesting for math. He tries to make you feel you could figure it out yourself. A blog of his mentions that the Soviet system was more about problem solving than the American system.

Likewise, there are many sources of intuitive online physics at many levels. Here are a few examples. Veritasium, Minute Physics, Don Lincoln, Sean Carroll's blog, HyperPhysics, David Tong's online lecture notes, Leanard Susskind's Theoretical Minimum courses, and many many more.

Following historical approaches is not necessarily the clearest. Newton and Principia are a particularly good example of why. Newton was brilliant, but secretive. His thought processes were sometimes convoluted. Newton invented calculus using fluxions and similar ideas. These are no longer used. The math has been made more rigorous and clearer over the centuries since Newton.

Intuition is very helpful to understand physics. But physics is full of notoriously counter intuitive ideas. It can and does lead people in the wrong direction when studying relativity and quantum mechanics. For example, see How can a red light photon be different from a blue light photon?

You have to be able to make progress when intuition fails. People have found that using formalisms gets you farther than intuition.

Still, intuition is really satisfying when your every day experience leads you in the right direction.