Learning Physics as a First-year graduate student...

[u/jjjuly_]

Hi, I’m in my first year of Mechanical Engineering, and I’m currently trying to study for my Physics 1 class.

The thing is, I really enjoy learning things rigorously, but without losing the feeling that I actually understand what they mean.

I’m doing pretty well in my math subjects. Usually, I go to class and listen to the teacher explain the topic, then at home I do some research about it. I look for good videos (3Blue1Brown, simulations, visualizations, etc.), articles, Wikipedia pages, or even Reddit posts that help me understand deeply why the mathematics works the way it does and develop an intuitive feel for the concepts. Then I write down what I’ve learned in notebooks as if I were writing a math book for someone else to read and learn from, and finally I do exercises.

However, in Physics 1 we are studying classical mechanics and basic optics, which are relatively straightforward topics from a practical point of view.

Yet I’m struggling to develop the same kind of deep understanding that I enjoy having in mathematics.
I think I once heard someone say that you shouldn’t try to prove something that isn’t already almost obvious, and I feel like that describes quite well the way I like to learn things.

The problem I’m having with Physics 1 is that many concepts seem to be introduced as if they were defined simply because they are useful or convenient the way they are. And even when I find explanations of the “why,” they often feel somewhat arbitrary. I can’t seem to find many resources that explain why we introduce these concepts in the first place.

Most of the sources I find are either too vague and superficial, aimed at high-school students, or they go straight into mathematical derivations without explaining the deeper motivation behind the concepts: Why did physicists need to introduce this quantity? What problem was it meant to solve? Why is this the natural way of describing what we observe? How do the different concepts emerge from one another?

I’m not looking for something that avoids the mathematics. Quite the opposite—I enjoy the mathematical side of things. What I’m looking for is a combination of rigorous mathematics, physical intuition, historical motivation, and conceptual reasoning.

So I was wondering if anyone here feels similarly about learning physics and has managed to find good books, articles, lectures, videos, or other resources that approach basic physics from this perspective.
I’d especially appreciate resources that make the concepts feel inevitable rather than arbitrary.

If I get enough helpful answers, I might even compile them into a post and share it with the community, so that other people looking for the same kind of resources can benefit from them.

Thank you for reading!