Pretty much all the classic Newtonian formulae you memorize in high school physics classes can be derived (relatively) easily once you bring calculus in. A general problem with high school classes in particular--still somewhat true in certain university classes but much fewer--is that there are dependencies across classes. So you end up with a lot of "Memorize this thing because you don't have an advanced enough background to understand why $XYZ is the case."
In my high school experience, this was avoided if you had the desire and aptitude to just take Honors Physics instead.
To work around the fact that many of us were still in precalc, our teacher just taught us the power rule, the relationship between slopes of tangent lines, etc., without diving into the "why" of why those things worked.
That said, yeah maybe for the most basic of university of physics the whole "derive it on the fly" strategy works, I guess? But when you get to more advanced courses like mechanics of materials, you'll do yourself the favor and take to memorizing at least a few of the commonly used equations.
For tests and the like, when I was an undergrad, it was fairly common to be able to bring in a one-page "cheat sheet." The idea was that you probably could derive a lot of the stuff given time and maybe references, but you almost certainly couldn't in a 1 hour exam in addition to solving the actual problems on the test.
I'm trying to remember when I had one of those last!
I actually don't love the idea of cheat-sheets but maaaybe if it's a cumulative final I could see it being helpful? If you're taking chapter exams on some material, I think you ought to have worked enough problems so that formulas/constants are drilled into your head. But I guess too, where do you draw the line at engineering appendices? I sure don't have the MoI of every common body memorized.
> If you're taking chapter exams on some material, I think you ought to have worked enough problems so that formulas/constants are drilled into your head.
Well, sure, but, if you don't, then what's the point of punishing you? As a teacher, frankly, I'd be happy to have my students bring in any static resources they wanted to consult—I say 'static' to emphasise not, e.g., consulting a cheating site, although it's fine with me if they've pre-compiled solutions in advance to any problems they think might be interesting or important—except that (1) I think that would encourage bad study habits, and, more importantly, (2) it would be unwieldy in a packed classroom to try to have adjacent people juggling multiple textbooks, notebooks, etc.
In fact, I loved the freedom to give extended-time, fully open-book, open-note exams during the fully remote classes. I wish I could still do that; if cheating weren't so endemic under those conditions, then I would.
Generally for stem test for application of material not memorization (Medicine you need both, etc). My lower level undergrad math courses all allowed us to bring a crib sheet with equations. It helps you go back over and study/relearn. In the graduate math / physics courses a crib sheet was provided and standardized. Memorizing final PDE solutions or things like Laplace Transform tables is no bueno.
Okay I'm just a systems engineer so certainly my material isn't as intense--fair points. I just didn't care for the explicit lack of rigor I encountered in my linear algebra class. I got a 94% and I can't remember anything.
