Most Collisions Are Secretly in One Dimension

This video is about elastic and inelastic collisions in 1D, 2D and 3D - and how the collision of conservation of energy with conservation of momentum, plus a secret direction, results in a completely predetermined behavior for most collisions.

REFERENCES

1D Collision Calculator:

Elastic collision of spheres Wolfram

Oblique collisions of two 2D spheres

Ballistic Pendulum


MinutePhysics is on twitter - @minutephysics

Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute!

Created by Henry Reich

[EebstertheGreat]

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.

[hendo]

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

[LookingGlassUniverse]

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.

[EgoLTR]

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

[victrmike]

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.

[Yupppi]

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.

[faffod]

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.

[Leonardo-G]

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.

[hukuzatuna]

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....

[octaviosilva]

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

Newtonian Mechanics lol

[TheRexisFern]

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

[blazernitrox]

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.

[angeluslupus]

Look - if you're going to keep putting up "well, technically..." and other such caveats, PLEASE leave them up for more than a millisecond!

[PopcornColonelx]

Incredible animation this time! Great work!

[taconator]

This is a fantastic way of introducing and understanding vectors imo

[sanderbos]

Awesome, loved the explanation and the animation!

[KarimMaassen]

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.

[masterdj]

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

[Roberto-couk]

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

[SporkleBM]

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 ✨