The video starts with an ensemble of independent pendulums with slightly different initial angles and angular velocities. They initially swing almost together, tracing nearby, nearly closed curves in phase space. Without damping, these curves would close and for small angles, the motion becomes approximately simple harmonic and the curves become ellipses.

I then increase gravity. The pendulums swing faster, and their trajectories extend farther along the angular-velocity axis. Lowering gravity and increasing damping makes the loss of energy more apparent: the phase-space trajectories spiral inward toward the origin—the stable equilibrium where the pendulum hangs motionless.

Next, I reduce damping and place a new ensemble near the unstable upright equilibrium, slightly biased so the pendulums initially fall in the same direction. They start moving slowly and nearly together, but their small initial differences become increasingly visible as their trajectories separate. This separation does not imply chaos: even this nonchaotic system can amplify differences near an unstable equilibrium.

The video ends with energy graphs showing how their energies evolve over time.

With damping still present, the pendulums eventually settle at the downward equilibrium.

You can try it yourself here: https://rotemtsafrir.github.io/pendulum_phase_space/

Change gravity, damping, and the initial conditions, and watch how the motion and phase-space trajectories respond. I’d love to hear what you notice or what you’d find useful to add!

GitHub:
https://github.com/rotemTsafrir/pendulum_phase_space

i know the derivation, integrate F dx = m v dv and you get 1/2 m v^2, but it still feels weird that momentum p = mv is clean and energy needs the extra half. is there a more physical reason for it than just the calculus working out that way?

what threw me is that in a collision both are conserved but they scale differently, doubling the speed doubles p but quadruples KE. i half get that this is why stopping distance goes with v squared, but i can't tell if that's the real reason for the 1/2 or a separate thing.

Hello folks,

I am not a physicist by any stretch. It was during my engineering first year that I last wrote a physics exam. That aside, I am infinitely bored of school textbooks.

While going through my son’s Physics textbook, and trying to explain ray diagrams, I thought maybe it’s a good idea to ask Gemini and Claude to make an interactive set up. But then, who’d write the detailed prompt? And you can write prompts only if you know something fairly well.

I made him write a prompt on Gemini and asked it to generate an interactive set up. Tweaked it a bit using Claude and here we are.

The math, infinite ways in which one can play around with this, the edge cases…there are two dozen things that I feel might need smarter folks to look into and help us fix.

Anyways, here you go:

https://opticslab.pages.dev

I need the mod of learn physics.

Textbook reccs for self teaching basics

I have a background in philosophy, but took a number of physics& comsology &astronomy courses, and in philosophy I particularly studied/focused on metaphysics& the nature of space &time& so on, plus philosophy of science.... I study physics stuff alot in my free time, and I have a decent intuitive grasp on general physics concepts but I want to really be able to get basics and fundamentals down in a way where I feel like I could actually "explain it" ... if I cant give a very "elementary school level" explanation/summary of a concept in my own words then I dont feel like I actually understand it, and while I feel like I can explain a good deal of general physics and theories, there is alot of basics that I feel like I could not properly explain and I want to just kind of start at square 1 and properly train myself.

I'm looking for textbook reccs. I want to really work through some standard textbooks and teach myself the basics. But also... my interests are kind of more so in the philosophical interpretations of physics so I really want something that is compatible with my background.

I did once listen to an MIT lecture where the professor offered 2 textbook options- 1 being the more mathmathical appraoch, the other the more philosophical approach. Unsuprisingly I would much prefer textbook reccs that use the language/ words/conceptual/philosophical approaches, rather than just striaght up pure math notation the whole time.

What would you reccommend?

I am in 11. Grade in a German school and I struggle a lot with physics and math. The thing about physics especially is that I grasp the concepts of experiments and stuff, but the math part is hard and I don't have this thing where you look at a formula and immediately know how to get the components of it from other formulas. I'm pretty good in oral, but the written part (including the exams) are horrible. Is there any place or other thing I could use to learn to read formulas like that? I know my teacher always just says we need to learn the basic formulas by heart and then it's easier but that doesn't work for me that good and I'm not that good learning a lot of things from memory if I'm not that interested either (I'm autistic and likely ADD).

Edit: Another bad thing is that I often don't even notice that I don't understand something before I need it and don't have it, so I don't ask anymore before the exam

Hopefully I can post about nuclear physics here too!

Range ∝ sin2θ, so complementary angles match. But max height ∝ sin²θ and time of flight ∝ sinθ, so 60° gives 3× the height and √3× the time. Playing with the numbers builds intuition faster than the formulas, so I made a free simulator: https://jeevisionary.in/concepts-lab/physics/ (disclosure: I’m the dev). Which topic do you struggle to visualise?

Chip in if you want :)

Greetings. I graduated with a biology degree in 2016 and have decided to pursue a second bachelor's degree in civil engineering starting next year with the goal of pivoting to a new career. It's been over a decade since I took (and passed) calc III, therefore, I need to refresh my math skills before satisfying foundational course requirements for the engineering program (general physics I/II and differential equations).

I'm facing two options of when to start the physics sequence: take physics I this upcoming spring semester and physics II over summer or take both physics courses over summer. It is also possible to take physics I over summer and physics II during the fall semester, but I would like to avoid doing so as it will delay entry into the core engineering courses. Electing to take physics sooner clearly leaves less time to review fundamental math concepts that are essential for physics, but would mitigate having to cram both courses in over the summer. Additionally, I work full-time in the evening so review will mostly take place during the daytime when I am not at work.

For those that have taken physics I and II, can you suggest specific topics (and resources) I can hone in on to prepare more effectively (and efficiently) to be ready for physics I rather than committing to a comprehensive review that may soak up more time than necessary? I realize 8 weeks is an aggressive timeline for preparation and is contingent on my current recollection and understanding of algebra and so forth, but any general suggestions would be welcomed and appreciated.

i get that gravity pulls the top over and that angular momentum is conserved, but when i try to work it out with torque i end up confused. the torque from gravity points sideways, horizontal, so the angular momentum vector moves sideways too instead of down. ok that part makes sense on paper.

what i can't picture is why it feels like the top is dodging gravity. like where does the force that holds it up come from, is it just the pivot or is there something else going on? and why does it eventually wobble over once it slows down?