Most Collisions Are Secretly in One Dimension 

The equations you showed actually have two solutions, which makes sense, because the energy equation is quadratic. For a perfectly elastic collision, the other solution is that the objects just pass through each other unaffected, which of course also conserves momentum and kinetic energy.

Wow, 5 months with no video and then i stumble across this one minute after it goes live

I love it when there's a sentence or two of text added on screen and it flashes for a bat of an eye so I have to rewind twice and then accept I need to pause on the third rewind.

Great video, and it’s so good to see you back! I’d never considered that fact that even when there’s energy loss, conservation of momentum and energy uniquely pin down the velocities. And I hadn’t heard of the secret axis of collision either, but it makes so much sense! Feels like these two points should be added to kinematics classes.

As a somebody who deals with computer simulations of mechanical systems for living, I can assure that simulation of collisions is actually a really complicated topic. If you have a system of multiple interconnected bodies, i.e. you are dealing with multibody system dynamics (that is the scientific keyword here), you can no longer deal with mass and velocity only, but instead you are, usually, solving accelerations from a system of nonlinear differential equations that describe the dynamic force equilibrium of the system. Contacts are treated as external forces, which means you need to be able to solve both the magnitude and the direction of the force, which is not a trivial task when the shape of the object is complex. Also, for contacts to be actually any useful, you need to model the friction forces at the contact points, which is not exactly trivial either, since, among other reasons, many models fail to create any force at zero velocity. In total, this means any contact can need, depending on the models used, 4-8 individually tuned parameters to work. Of course, if you are making a video game, things can get a lot simpler since accuracy doesn't really matter. But for an accurate simulation that you could use for engineering purposes, things are quite different.

Great video but all those flashing texts are a bit annoying. I love to read the extra complexity you put in the notes but on a phone or smart TV it's almost impossible to pause at the exact right time. Please keep them in the screen (a bit) longer in the future

I remember having to figure exactly this out when making a physics simulation for coding practice. At first I had no idea how I was going to handle collisions in 2D, but then I realized I could simply look at the collision from the frame of reference of the two colliding objects (ie their total center of mass) and that simplifies things to one dimension.

So glad to see Minute Physics back! Thank you. And though I don't know how much more it takes to animate, I think that the animations are a great addition. I would ask that your *caveats and *clarifications be more than 1 frame, it is distracting trying to scrub to find the one frame that had something I wanted to read.

This is one of the first video by minute physics where I actually know and understand what they are talking about Newtonian Mechanics lol

I'd love to see the same kind of video for rotating objects - spinning tops colliding, theoretical spinning spheres, maybe touch on spinning black holes....

I'd never thought of it this way. One of the first things we were taught in High School (AP) Physics when it came to collisions was that you always separate the vectors into their components, but it never occurred to me that essentially we were computing a 1-dimensional collision.

Incredible animation this time! Great work!

This is a fantastic way of introducing and understanding vectors imo

Awesome, loved the explanation and the animation!

Very cool video on the basics of kinematics of collisions. Love it!

It's all really simple, but also complicated. You know, science.

Glad to see minute physics again! And this time I understand more of this concept because I'm actually learning it in college now! So that's really neat ✨

great to have you back ! you rock dude! :P

Great to see a new video from you!

The animations were so cool! :) Do it again!

I was internally screaming "what about rotations!" the entire video, but then I sighed in relief when I saw the note at the end.

And again, I need to watch your movie twice. First time I'm just totally locked in to the awesome bass backing track

Great work 🥳Thank you 💜

This is the secret to physics: It's not hard, just pretty damn tedious

Yay! You're back! What were you doing, Henry?

Great explanation brother.

Wowwww. It was such a long time minutephysics uploaded a video! Even though minutephysics have more science that other people can bear, it’s still great!

You should make part 2 for this video which will explain rotations. I really love Newtonian mechanics!

Firstly, this was a fantastic video and I really appreciate the effort put in. Im going to watch more videos from this channel for sure. I do think that the *captions should be visible for longer though. Unless I'm not aware of a method that makes it easier to pause within a particularly small time interval, I really think they should be up for longer 😅 it's more than likely because I'm dyslexic and can't read quick enough but I doubt I am alone. Thanks for the great video!

This is the first video I saw and I subscribed 🔥🔥

That was a really fun insight!

Great vid! Just a little remark: Those side notes flash by way too fast. I don’t want to stop the video, scroll back to the exact frame it was shown.

Bro, you should have made this 5 years ago when I was studying collisions in Physics. This definitely would have helped.

Great video! If we ignore all the reasons multi-dimensional collisions aren't one-dimensional, they are secretly one-dimensional! The profundity here boggles the mind!

My physics teacher showed us a way to calculate collisions by switching to the center of mass's frame of reference, which a) turns the problem into a 1D collision and b) is really easy to solve then convert back to the lab frame.

❤❤❤❤minute physics is love... I commented about your absence on your recent community post yesterday, and here you r today

its been a while since ive looked at one of your videos. I still remember back when i was watching you channel, CGP grey, and Vsauce.

Excellent video!!

This basic physics but presented with beauty !

another great vid. thanks

YES! I waited for this

I'm glad to see you back! By a crazy coincidence, I stumbled upon your channel yesterday and was surprised to discover you haven't posted on social media for 5 months. Your content was missing a lot ❤️

All the collisions at the end were so satisfying to watch

Love your channel!

Welcome back man

Really good!!

We have been trying to realistically simulate collisions with computers for more than 30 years now, and we still have to use hacks, like virtual thickening of surfaces, smoothing out surfaces and their motions etc. When you measure time in discrete intervals collisions are a lot more complicated. In order to know where the "hidden axis" is, you need to know the exact moment of collision, which is near-impossible in a system where time is discrete and of limited resolution.

The animation looked awesome. Does anyone know what software is being used for these?

I think you put it brilliantly my friend. Scattering and subsequent spin variations I find less important. I know people want to know exactly what is going on with all the composite particles of the collision, but the predetermined mechanism is clearly there and the spin variations are likely do to mass clumps

Excellent!!

This is AMAZING!!!

It's cute that you have those single frame footnotes, but it's only a distraction when not stopping to read them and a nuisance when you have to interrupt the flow of the video every 10 seconds or so. And it's pain on mobile. Maybe scoot them over to captions?

Thank you!

The amount of split-second footnotes showing up seemingly every second of this video really makes this video feel like a drug ad. "It's simple!" followed by a minute of disclaimers.

U r really amazing minute physics 🥇

Great video! Question: does this not just follow trivially from a change of basis vectors? Or am I misunderstanding the result!

minute physics, millisecond notes.

I hated science in school, but your enthusiasm & interesting tid bits make it easy for me learn & grow my opinions :)

You missed a great opportunity to explain that, in fact, there are 2 solutions for the conservation of momentum equation. One is what you presented. The other one is to keep both velocities the same as they were before the collision. It's not physically possible, but it's a valid solution for the formula.

Many years ago I came up with idea, that there's no such a thing as "random". That's the concept that allow us to comprehend thing we don't understand. If we could have a power to define every single possible variable of any event, we could tell the outcome of that event.

I learned this in dynamics but it's cool to hear from a different perspective

That reminds me of when I got rear-ended by a Toyota Tundra. My Dodge Stratus was the stationary object at the light, the Toyota tundra was traveling at about 50mph and did not apply the brakes. My car slid forward about 10 ft. The Tundra collided with us again, sliding us forward another 10 ft and folding the trunk lid through the back window. The Tundra collided with us a third time and buried itself to my back tires, finally bringing this abbreviated Newton's Cradle to a screeching halt. The driver offered me any amount of money to let him leave the scene of the accident. I asked you've been drinking, haven't you? He admitted as much, and his breathalyzer results were just barely over the legal limit. There were five other vacant lanes he could have swerved into if his excuse of, oh the brakes weren't working, were valid.

Dimensions are (in other words) directions, time can also be considered a direction ('arrow of time' for example). So a way to interpret this video is a single dimension plus a time component.

Yay. New content!!

Sir, you just inspired me to make a collision simulation. (in my beloved C++/SFML of course)

Woo Minuephysics is back

ah, a "back to basics" minute physics video. It's why I subscribed in the first place!

The little caveat pop ups felt WAY too fast. I can usually pause quick enough to read them but I had to rewind for each one this video.

That part at the end. I love it. Omg

that ending was very satisfying to watch

What about colloision of matter and antimatter? please make a video on superposition principle..

NIce. A genuine question triggered by your very first example at 0:48. When one object hits a stationary and both have the same mass, the first one stops, the second one moves on at the same speed as first one. Conservation. But .. so it would be if, for example, the first one continued at 1/3 the speed and the second at 2/3, or any other matching set. And with the m and m.20 example next, why not the m stops fully (rather than rebounds) and the second goes at 1/20th which would be more in keeping with the first example, eg the moving mass imparts all its momentum to the mass it hits.

This is relaxing

I wish you would talk more about numbers of variables (V) and numbers of equations (E) for multiparticle systems and confirming or disproving that V=E. Because I worked on this problem, trying to calculate in general, and I could never get V to equal E. I always had V > E. So every collision problem I had with more than 2 particles and in 3 dimensions was underdetermined.

Interesting, I didn't think about this^^

The end of the video was really good

Welcome back luv u

0:46 Holy shit. how did you even do that animation?!

I suspect that in reality there is probably a great deal about the science in your videos that I don't understand because, you know, maths. But ignorance is bliss and I still enjoy them and look forward to them because I always learn something.

I have fallen in love with this kind of Physical thinking. The work of David Hestenes "Geometric Calculus" works to formulate all physics with the dynamical vectors as the basis. It makes these realizations much more apparent. 10/10 recommend

@1:48 Is there a way to definitively calculate this "secret direction" you mention - assuming objects of weird shapes/sizes and frictions? I'm curious whether this is the kind of thing where sufficiently-unusual shapes/friction would require computer modeling and/or real world observation to figure out, or if there's any formulas that can be worked out by hand to solve any given instance?

I know the channel is called “minutephysics”, but could you make more 10-15 minute videos? I feel like this just scratches the surface.

"In our universe, the equations have a unique solution" surely there couldn't even hypothetically be a universe where the logical deductions involved were invalid?

Was thinking about this the other day- two photons colliding, and realised that without something weird and 2D happening, there's not actually a meaningful distinction between colliding and phasing through.

What did you used for the collisions ?

A new minutephysics video? Am I dreaming?

Back in high school I was very weirdly obsessed with physics engines for games, can't believe how much time I spent on these equations. Thinking about them still makes me feel giddy. Then I had advanced dynamics as a post-grad, life changing most fascinating shit I ever studied. Also the most difficult.

Macroscopic collisions also have friction, but still, the sum normal + friction points in a single direction. We do need to allow for rotational energy in that case. Long-ranged interactions with energy loss/gain; however, can be asymmetric.

These days videos are sparse...it's always a pleasant surprise when I get the minute physics new video notification

Very cool! But how do you find the secret direction for a given 2d collision?

Ngl I first thought this was an old video until I saw "19 mins ago". Great animations.

Welcome back!

Which physics engine did you use for your animations?

Super interesting. Does this all mean that brownian motion is deterministic, or the extrapolation is not valid? I am genuinely curious.

I’m going to try this on my next physics test, wish me luck!

This had to be one of the funnest videos to make with the animations.

I remember your first film and i wil remember the last. Thanks for everything

I think this video has the most side notes of any Minute Physics video

This would have been a great complement to my first kinematics class in high school.

Correct me if I'm wrong but are the examples here just perfectly elastic? We have the case where one of the objects become embedded in the other, which Im surprised isn't even mentioned