The Maths of Spinning Coins and Euler's Disk
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- Опубликовано: 20 мар 2016
- A spinning coin rotates as it wobbles. The rate of rotation is (1/cos(θ) - 1) of the rate of wobble. Draw an arrow on a coin and check it yourself!
The notes from the whiteboard are available here:
imgur.com/a/XVw6m
Here are the videos of the disk spinning:
NORMAL SPEED: • Euler's Disk: normal s...
10% SPEED: • Euler's Disk: 10% speed
Music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Maths book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/ 
Развлечения
now THAT is what I call creative use of video.
+proefslak You know what, before today I always found him kind of dry anytime I saw him on numberphile. In fact, I always found numberphile kind of boring compared to others Brady channel.
This video was suggested to me today, I was not subscribed to him. But this video is something else! It is funny, entertaining. It is both educative and intelligent and well made at the same time. The way that he timed his explanation for the time it took for the Euler disk to come to a rest, the way he finished it just in time to come and see the end with the viewer at the end. Perfect!
I watch a few of his other videos and he definitely earned my subscriptions! I would even be ready to put money towards his videos on Patreon but I guess we will never see that happening due to his position in academia.
Anyway, great video overall and probably the best Euler's disk video on YT I was.
This video helped me find out that my left speaker wasn't working!
Lmao
dont be racist sinz
the marble racer it’s ok! Your speaker is most likely hooked up mono instead of stereo. So, in other words, you get left and right in one speaker.
Unless... your left speaker is actually missing or damaged.
If so... You can just take the wire that was originally connected to the missing or damaged left speaker and attach it to the same place where the right speaker wire is attached to on the right speaker.
If you do this you will hear right and left sound in the same speaker.
SinZ , You missed the intellectual part, dude.
Same for me, but I already knew than the left one wasn't working and I was not really satisfied since I want to see the maths :(
I did not expect the wobble to last the explanation.
These are stand-up maths.
you underestimate the power of maths.
how many trials before it gets that perfect, though?
I didn't expect the explanation to last the wobble
I really appreciate that perfect timing of the wobble and the explanation. Well played, good sir.
This video is a masterpiece
That’s a long neck at 1:32.
NOPE.avi
LEL
"some of you just want to want to watch the disc spin all the way down" I cracked up, exactly me
Sean Haggard 100th like
4:44 was the moment i realized this is the most awesome video i watched in my whole life
There's a third group of people: those of us who just like watching you explain shit.
I should start a new channel of "Matt's drawn-out explanations".
@@standupmaths yes you should
@@standupmaths I'd subscribe.
4:44 You felt like a rockstar for second didn't you ? :D
I rocked that disk.
Many camera zoon lenses use an ultrasonic motor to create the Euler-wobble effect in a ring, which drives the lens round, extending or retracting it very quickly and very quietly without adding a bulky motor to the lens.
Awesome. Thank you.
Oh... that must be the ultrasonic motor camera manufacturers refer in the ads. Never did I know it was using Euler-wobble effect.
Oh man That timing *applause*
Beautiful timing.
holy shot that timing
That's one hell of a creative video. Fantastic. Hard to see something that is that so thought out and well timed on RUclips. The way you basically merged two contents into one, even splitting the sound into two different speakers, and timed both activities in a way that they match. It comes over as so simple, yet so effective. And it's genuinely funny.
Well done.
That moment when you realize the traced circle is a section of a sphere with the same radius and center as the disc. 😳💥
Mind = blown
The most amazing thing is how much I learned with only 8 minutes of video.
1:50 i belong to both groups. :D
You're going to have to use both ears then.
Me too
It's crazy how the motion looks so complicated but it's described by a pretty simple relationship. Awesome video!
im a big fan of your work matt! glad i found your channel and ill be watching for more videos. thanks for making math fun!
Oh ! and it's also doing a revolution around the center of the disc-plate-mirror thing !
Another ratio(s) to calculate :)
4:41 the sound of perfection :)
YAAAASSS!!
this video was beyond amazing, the topic, the aesthetics, the editing, everything
Argh! I want to hear the explanation of the math(s), but my left earbud is broken! All I can hear is: "circumference" SHHH-KWUB SHHH-KUWB SHHH-KUWB, "pi R" SHHH-KWUB SHHH-KUWB SHHH-KUWB, "angle" shhh-KWUH-KUWH-KUWH-KWUH-KUWH-KUWH...
Same, hahahaha.
Parker earbud.
4:41 The disk is about to enter hyperspace.
Nice video! The best part is that by the time it stops wobbling, you finish your calculation! Great timing!
Loved the audio trickery in this one!
such a climatic ending, it kept me interested 👏👏👏
Yes, me too
That was fantastic timing!
Man I was on the edge of my seat. Way to make maths dramatic. Also excellent choice in music.
Cool content, cool presentation! Can't appreciate the effort you guys put in enough.
I teach Maths to Fifth Level students who 'H A T E M A T H S' (their words, not mine.)
They love your videos, though.
Since I've been showing your videos, their Scores have improved.
Thank you.
Fantastic! Thanks for letting me know; I feel less guilty about not being a real teacher anymore. If you want a video message to your class, send me an email.
High speed slow mo is my favourite mo.
+TVFILMBUFF Moe is my favourite of the three Stooges.
Great timing with the math on the board and the spin. I like the song too.
Your (my) Book A Mathematicians Journey through Narcissistic Numbers, Optimal Dating Algorithms, at least Two Kinds of Infinity, and More is "Great" and much larger than expected. Thanks for writing it.
FYI:
Feynman actually said in an interview:
“I was in the cafeteria and some guy, fooling around, throws a plate in the
air. As the plate went up in the air I saw it wobble, and I noticed the red
medallion of Cornell on the plate going around. It was pretty obvious to me
that the medallion went around faster than the wobbling.
I had nothing to do, so I start figuring out the motion of the rotating plate.
I discover that when the angle is very slight, the medallion rotates twice as
fast as the wobble rate - two to one. It came out of a complicated equation!
I went on to work out equations for wobbles. Then I thought about how the
electron orbits start to move in relativity. Then there’s the Dirac equation
in electrodynamics. And then quantum electrodynamics. And before I knew
it....the whole business that I got the Nobel prize for came from that piddling
around with the wobbling plate.”
Although he was correct about QED, he was wrong about the rotating disk it appears.
Oh well we can forgive him ... xD
He was not wrong... the disk was thrown in the air, while the Euler disk was on the table, and hence, was experience the normal force, something which was not being exerted on the disk Feynman saw. Come on dude, that guy was a professional physicist!
Great fun fact, and insight onto inspiration.
Watched once for the disk, rewound and watched again for the maths.
You are a monster for interrupting the disk the first couple of times though. It should be against the law to stop Euler's disk while it is spinning.
This is pretty cool :) thank you for spinning things, Matt!
That beautiful moment at 7:30 where the wobble matched the BPM of the music.
The spinning disk made such a wonderful sound :O
Also, interesting mathematics too ( ;
your math is ok for a basic calculations in ideal conditions, but the inner "circle" is actually a spiral. the disc is actually rolling forward while falling to the side. at any point in time the disc is attempting to slide out at the point of contact, so the coefficient of friction between the materials comes into account.
imagine the disc were simply placed on the table without being spun at any angle from 0° to 90°. the center of gravity of the disc would fall straight down with zero friction with the edge sliding out, but if there was total friction the disc would fall along a curve whose center would be the point of contact. any friction between these two extremes would result in some amount of slippage.
to be complete, you must also consider the disc spinning on end before it begins the wobble (or the rolling path that initiated the wobble. either way there is an initial impetus that must be quantified. was the disc spun hard or softly? did someone flick the disc to make it perform in a certain manner? if spun perfectly upright, the disc would slow down due to friction (and don't forget air resistance) but remain balanced on edge when it stopped , assuming a level surface. if spun at an angle, the spinning perimeter would lie beneath the surface, which would affect the trajectory as the coin slides and bounces until eventually reaching an "upright" position. thus, the initial impetus of a spinning disc is varied and must be considered. a disc can begin a spin in multiple fashions such as rolling, throwing, dropping, or being struck, all with varying results.
plus the disc's dimensions could be altered. if wider it could be considered cylindrical. complete computations would also cover spinning rods and all potential cylinder based dimensions.
You're killing me. Brilliant idea, perfect execution.
What a nice video and so amazingly done. Good job man!
How did you time that so well?
+mrwho995 He didn't show us all of the previous takes ;)
+mrwho995 Probably by doing a whole bunch of takes until one happened to have good timing.
+mrwho995
I assume he's gotten used to what sounds like, so if he hears the disk getting higher in pitch, he knows when he needs to start wrapping up his explanation.
who else thinks that he should be the next doctor?
+Nick Schofield (Science n' Stuff) yespls
amazing as ever, Matt
All of my favourite channels are linked together! Tim was just showing off a Euler's disk! :D Grand Illusions!
nice timing also
Hey Matt, you could save yourself a syllable if you use Tau instead of 2Pi just sayin'
That's the weakest argument for Tau I've personally ever heard. Reminds me of the scene in South Park where the guy on the home shopping network talks about the billions of dollars he is saving his customers by saying "E Pay" instead of "EZ Pay".
***** My comment is just a joke on the fact that Matt hates Tau
Rob Mckennie Ah the joke flew over my head
Man that was intense! Keep being great Matt!
Thanks dude! I have been looking for a video on this since forever.
I'd love to see a simulation showing the path of a point on the circumference of the disc as it traces a shape. (Would it be a corkscrew? What *would* it make?)
this is all fine and dandy but we're not accounting for the filleted edge of the disc
lol
Great take with the spindown finishing at the end of the explanation.
Thank you for pronouncing Euler properly. Took me half of my first year to figure out who this Yuler was that people kept talking about.
You need to get your hands on some 360° cameras. This video already was some creative use of the tech you currently have available, can't wait to see how this goes in VR.
+Leo Wattenberg (LEOXD) A 360 degree video wouldn't really help, as they are set in a fixed position, and as you would most likely watch one part of the video - the spinning disk, it would be a waste.
What I think you meant is to have a way of producing videos in 3D space, i.e., in which you yourself could change the position and angle of the camera, so you would be able to, say, walk around the table, instead of just being able to turn around and see what is opposite the table (360 degree video).
Though that is commercially impossible, as YT does not support that, and I do not know how it would be possible to model such a big space in 240 fps (one would also need a dedicated player to watch such videos).
Or one smart person could create a realistic 3D model in some rendering program with physics (I believe that would be the closest you could get to the idea you're proposing, though it would most likely be not 100% true to real life).
JamesHD1990 oh, I'm not talking about this particular video. But I recon that Matt could use a 360° camera creatively enough for other videos.
Now I know where Joust got its sound effects.
So satisfying. Also, the end was a perfect music video.
Hands down... Probably one of my favorite videos of all time.... Then again.... I say that every time
Y u no sec(θ)?
I considered it, but would add to the explanation.
+standupmaths I have invented a mathematical formula. How can I claim credit for it?
+inakilbss Be the first to publish a paper for your formula in a maths journal?
+letao12 Thanks for the idea. I don't know why I didn't think of that.
+standupmaths Could you do a follow-up video, showing the relation (if any) between the disk's radius, thickness and/or mass?
Think I went on some kind of drug trip at 6:20
+MrHappyBollox How much time for mathamphetemine these days?
+Taylor Foulkrod You get locked in prism.
LOL
You were spolling hard on some E disk.
Nicely done. Really amazing stuff.
that stereo thing was great :D really nice timing!
What about the people that want to see both? :(
Watch it twice
you've got 2 eyes haven't you?
+TehJumpingJawa No..?
TehJumpingJawa I can only look in one direction... :P
That disk gives me so much anxiety i just want it to stop spinning but it doesn't and drives me INSANE this video stressed me the fuck out hahaha XD
Here's my advice: don't watch the full slo-mo video.
+standupmaths Haha, yeah that would probably drive me to the brink of insanity. Love this video though!
I really had the biggest grin on my face as you set up the meat of the video and then executed perfectly!
I had a similar grin when it worked!
Man Ur videos are fantastic keep going
Isn't the angle consistently changing ?
You start with θ when the arrow touch the ground the 1st time, and end with θ - ϵ when it touches the ground the 2nd time.
Doesn't this effect the rotation ?
+Miahoo Didn't you watch the whole thing ? He points it out himself.
Rizos Christodoulou
I didn't notice. When?
+Miahoo Just after the 5:00 point.
What's the music you used called? I did check the description, but searching for Howard Carter did not help.
+I'm made of blueberry coffee.
Second that. I messaged Matt about the music but, sadly, never got a reply.
+I'm made of blueberry coffee. I've been looking for a while and can't find it either :(
It is custom music Howard made for me. We'll release it properly eventually.
+standupmaths -.- Thank you! It's lovely!
Subscribed.
Love this channel.
I love you too.
Puts WAYYY to much effort into his videos. Underrated af
is there name for the theme song?
Algorhythm just look up standupmaths intro song, and you'll be goochie! ;)
BUT WHY IS THERE HAIR AROUND MY ANU-oops, sorry, wrong channel.
Around your annulus? No idea.
+LPSwimmer2011
Bravo.
+LPSwimmer2011 Plus they already answered it as much as possible.
+LPSwimmer2011 Dat Scishow reference tho.
Shubham Dhiman scishow reference
I was so excited to see you do some proper physics
:D this is hilarious, I knew about some vid. from you few days ago and put it to my later to see, now I was playing with coin and then I said myself there is yours math vid. I want to check so I came here and couldn't stop laughing about what I'm going to watch :D
You should use tau instead of 2*pi.
BLASPHEMY :p
#TauMasterRace
No. If you do physics as well that would be a disastrous inconsistency.
+Axel Bengtsson Why? Every formula you can write using tau instead of pi.
+pacinpm2 Also while solving higher grade differential equations? That just obstructs.
the good part starts here 6:21
Skiparino kripparino
+Ieuan Hunt Never thought I would see a Kripp reference here
+jresij we are everywhere buddy
Your videos are becoming more and higher quality you deserve 100,000 subs!
Just wait until I get some new filming equipment!
+standupmaths Hey sense your reaching 100,000 Subscribers. I wonder if you would ever do 2^x Subscriber specials thats what I going to do on my channel to standout and also I make the thumbnail for 1024 Subscribers 10,000,000,000 in base 2
Very interresting!
I do apprreciate your work!
A Tungsten Carbide disc on a Teflon-coated steel surface works much better than this steel on steel config.
Why you say that?
Why named Euler's disk. Did he invent disks? Or just the first to spin one?
+Mekratrig You could Google Euler's disk and learn about it then.
+Mekratrig Euler was the first to talk about this specific dynamic system of a spinning disc on a surface like this.
Everything is named after Euler. I've stopped questioning it.
6:47 Put it on full screen, go half crossed-eyed and line up the images to watch this bit in "3D".
This is like a performance art video. Super!
what's an euler's disk? shouldnt this be the first thing to explain in the video?
Well it's the disk in the video.
what a useful reply. what properties does it have? what's the definition? is every disk an euler's disk?
+p0gr Well, just re-watch the video, I'm sure you'll understand.
+p0gr Ok just kidding here, but you've got to admit that I, not knowing you, couldn't have known if you meant it literally (like "what is this disk he talks about? Is this some mathematical object involved in the calculations?") or not, actually asking what its properties were. And I didn't know the answer to the second choice so I chose to respond to the first one.
yeah, 'cause people watching maths videos usually are stupid like that.
Very well timed. Awesome vid. Thanks
Excellent performance! Bravo!
I love your videos.
The sound while that thing spins is amazing.
I honestly expected you to finish the math early and grab the disc. It made it so much more satisfying when it finally stopped.
7:46 You can see how indeed wobble rate goes up as the angle decreases and spinning gets faster and then starts to slow down as it goes to 0 wobble rate becomes infinitely wobbly for an infinitely small time before it completely stops right lmao you can listen to it at the end idk what i'm typing but the formula is fantastic, I kind of wanna graph it over time to see what kind of thing comes out of it
low math content but high awesomeness content.
Congrats, awesome video
Thank you so much for making this sir.
I've also realised that this is very similar to the math of a spinning hula-hoop, which I now intend to use for an animation soonish. Without this little formula I would've probably just faked it, and that wouldn't have been nearly as fun.
If you ever feel inspired to do a video on hula-hoop math, you would be my hero :)
(I have other nifty suggestions if you're ever looking for those, maybe I'll send an email)
The music is perfect. Props to that guy.
I wish all professors were like you. the enthusiasm you give about something as boring as this is crazy. well maybe partially because I love math but I have never had a professor how got me excited about it, in fact, a lot of the time they do the exact opposite they make me hate it because they never take the time to derive things from scratch it's just math magic and they just seem like they hate both us and their lives so it does quite add up
Beautiful explanation!
Fascinating video, as usual :)
So simple. So good. Great video!
Just so you know, I applauded.
enotdetcelfer 7:37 actually -;)
*This video helped me fall asleep. Thanks Euler!* 😴