Matt & Hugh: The Euler Disk Which Spins Forever

Matt and Hugh play with an Euler Disk which spins forever. Then they do some working out to check Matt’s previous calculations.
Matt’s previous video: The Maths of Spinning Coins and Euler's Disk
• The Maths of Spinning ...
Sadly we don’t have Euler Disks on Maths Gear but it is of course on Amazon:
www.amazon.com/Toysmith-79170...
Dr Hugh Hunt is a Senior Lecturer in Engineering at the University of Cambridge and a Fellow of Trinity College.
www.hughhunt.co.uk/
This is a new video format idea, so all feedback appreciated.
CORRECTIONS:
So far, none yet! Let me know if you spot anything.
Piano music is an original piece “The River” by Frode-5.
• The River - Original P...
All other music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/

[@Scy]

The sound at the end of the spin is so satisfying.

[@jattprime2927]

ikr

[@IIARROWS]

Sounded like it was ready for a wheelie.

[@mal2ksc]

It recalls the ZWIP! at the end of the black hole merger detected by LIGO, which was incredibly satisfying for other reasons.

[@LordDragox412]

Entering hyperspace :D

[@davidm.johnston8994]

Yeaaaah

[@Gabu_]

*_Matt & Guest_*_ Play with a thing and then do some working out_ should totally be a regular series.

[@kingxdedede7327]

This is the second episode, Matt & Hugh play with a Brick and derive Centripetal is the first.

[@vrixphillips]

LOL "finally, something named after Euler" "he's nearly forgotten" xD and people say mathematicians have no sense of humor

[@asthmen]

Euler who? Never heard of this guy. Mathsy, was he?

[@inna9882]

+Asthmen he is even has a number number named after him he also discovered that e^ipi=-1

[@vrixphillips]

that's the joke, though, Milos lol he has a LOT of stuff named for him.

[@inna9882]

Vrixton Phillips i know i was just answering Asthmen

[@__-nt2wh]

+phthisicy thats the joke...

[@2Cerealbox]

I really hope this is a long-running series just so I can see that intro again.

[@lovrebabajko]

+

[@NicklasUlvnas]

+

[@leepoling4897]

++

[@leepoling4897]

+++

[@leepoling4897]

+++++

[@Halosty45]

Matt is one of my favorite disk jockeys.

[@huruey]

8:44 Aw yeah dubstep!

[@mindfulmike8612]

underrated comment right here

[@Maxander2001]

LOL :)

[@sam08g16]

Hugh: that's the wowowowowo right? Matt: roro yeyeye

[@pcfreak1992]

Actually he said "wowowowo _rate_" ;-)

[@DlcEnergy]

woubwoubwoubwoub... get it right you failures of dubstep... ( ͡° ͜ʖ ͡°)

[@jarodboyd72]

"Should we have a race? 😁😁 I love you Matt.

[@JoaDrath]

" You lost this.

[@lxathu]

Now it's official: Matt is racist. He was always suspicious... always trying to find final solutions.

[@hydroweapon]

I see what you did there

[@farpointgamingdirect]

facepalm...

[@milos_radovanovic]

As to overengineering it, he can still add a stroboscope to it. :D

[@MrSimpsondennis]

you know, they say, "As the angle gets less, the wobbling rate gets bigger" so, could we state that when it's laying flat on the table it's wobbling at unseeable and unmeasurable rates? :p

[@hhaavvvvii]

If it wasn't for friction, yes.

[@TheAlison1456]

But it is? Its atoms are!

[@chaitanyabatra6952]

@@TheAlison1456 come on it's atoms are always in motion but their net motion is brownian not a travelling oscillatory wave just about y axis

[@chaitanyabatra6952]

friction results in flattening the system and making it wobble less so the wobble is approaching 0, and in the non perfect reality approaching 0 actually approaches 0 quite fast

[@lawrencecalablaster568]

Yay! This series is good, & I am very very happy that it's actually a series now :)

[@lawrencecalablaster568]

I love it when people talk about things that were named after Leonard Euler :)

[@mikewilliams6025]

Leonhard? I thought the disk was named after the great Gilbert Euler.

[@U014B]

+Mike Williams You sure it wasn't Houston Euler?

[@NeonsStyleHD]

I thought it was Ruler Euler da dum! Someone had to do it lol

[@TrimutiusToo]

Euler has a first name? Who knew? lol

[@michaels4340]

Did that h get autocorrected out?

[@mrcalligraphy2722]

Can we get a series where you two sit on a bench and ramble?

[@Vulcapyro]

Ask Tom Scott?

[@AntiGravityC9]

or ask jacksfilms _it's two nerds on a bench, it's two nerds on a bench_ _there's matt and then there's hugh and they're two nerds on a bench_

[@thekingoffailure9967]

+Anti-Gravity omg yes!

[@francoistrempe]

Super Interesting, but, minus 1point for using white paper

[@-.._.-_...-_.._-..__..._.-.-.-]

+MichaelKingsfordGray Minus one point to you for implying that Linguistics is not a science. What is wrong with using white paper, by the way?

[@all_time_Jelly_Fish]

He's an engineer, he knows assignments aren't accepted unless they are on engineering paper.

[@andywright8803]

... but this isn't numberphile, and I thought they had copyrighted the use of brown paper

[@absurdist5134]

As long as they don't get crayon on the walls it's fine. - Mother dearest

[@DANOVERBOARDvlogs]

Or Shaprie bleeding thru onto the table.

[@jekyllgaming99]

Please make a video showing why the best ratio of width to height of an Euler disk is around 6 to 1. I would love to know why this ratio is often considered the best 😀

[@healthystrongmuslim]

idk about most of this but well the ratio of circumference to radius is also around 6 to 1. (2π : 1) So there's that 😏

[@skilz8098]

I think 6:1 might depend on the composition of the object... Depending on the material that is used; its density, its surface texture {smoothness or roughness}, the amount of friction that it applies, and other properties that can be leading factors this ratio could change.

[@davidm.johnston8994]

Good channel Matt! So glad it's there to show a little bit to the world that math is fun.

[@cyral_u]

It almost looks like you were learning, looked like a kid for a second!

[@Neffers_UK]

This is the reason that the guys that know sh*t don't whine. They enjoy the fact they could be wrong, and revel in the fact they could be right. Having a conversation on your own level, be it mud pies. machinery or quantum physics is exciting for all involved. There's some human distraction from this perfect scenario however - it's not often you hear of two or more people discovering things, each will go about it their own way, which is even better - till some guy who is out of sight comes from their research and scoops it all up and makes something new.... it's all awesome. Gotta love it. I'm as thick as pig sh*t but I love trying my own dumb ass ways, fumbling around in my shed or on paper. I get giggles when I meet someone who has been through the same neanderthalic methods as myself and there's some unity. Oh, I rambled, sorry. Have a nice day :)

[@Liliou]

+Cyral Yeah so cute right! Especialy when he get proud of his demontration of the formula at 9:07 he's all like "look at me professor i'm a good one!" And +Neffers I enjoyed your rambling. :)

[@Maxander2001]

Good ramble ;)

[@ardenvarley-twyman8352]

+Neffers TL;DR.

[@charlesgoddard7026]

Love the Matt and Hugh vids. Great format, great contenr, great fun too

[@54321emb]

This was adorable to see Matt so candid as he works through a problem

[@Oxirix1207]

That was an amazing video!!! I love that he had an experiment set up for this.

[@RichardBrocklesby101]

I have no intention to ever replicate anything Matt does. nor do I really have any understanding (all although I nearly bought 72 pencils the other day).... so how is it that I find his videos so entertaining? LOVE IT. thanks Mr maths man.

[@giulianoluponio7811]

That, right at the end, was an absolutely beautiful sound.

[@krischurch5677]

Really enjoyable video - And its nice to see even Matt can end up looking like a schoolboy with a teacher even after years of Stand Up and presentations on mathematics. Makes the rest of us feel a little bit better :) Thanks guys

[@MrRoverno]

at 15:50 i love the circular patterns of light reflections on the discs as they spin/wobble.

[@RolandoGarza]

great episode... looked like lots of fun

[@thoperSought]

I didn't think it was possible for this one to be funnier than the first on you did. I love engineers. I really do.

[@jpaugh64]

The most exciting footage ever uploaded to KZbin! :-)

[@trains1000]

That sounds at the end is amazing.

[@marcmarc172]

H: I got a blank disk. The reason I like my blank disk- M: It's got- H: It makes it nice and easy t- M: easy to draw a circle. H: -draw a circle on it. M: yeah. H: And the idea is, that, so this little dot here, when its wobbling like this M: yeah H: you can see that dot- M: Yeah! H: is- M: that that H: tracing out a smaller circle. M: Yes. H: so that smaller circle, is where the edge of the disc is following that. M: yeah H: so the dot has moved from there- M: to there! H: to there. M: okay. H: lets call that angle theta looks like this scene took 10 tries to do, but STFU MATT AND LET HUGH TALK Source: 7:33

[@1019wc1019]

I think it's acceptable as he's British and I have found its more common to speak over eachother/finish the sentences.

[@genau14zeichen]

I think Matt was just so happy to have a good conversation about Euler disks and maths and he couldn't hold himself back.

[@jattprime2927]

they are so romantic, finishing each other's sentences. btw they called the angle beta cause theta was already tacken (last line of convo)

[@morethejamesx39]

I don't think he's being rude, he's just saying 'yeah' because Hugh's saying what was already in Matt's first video

[@damienw4958]

+PROTIP atTheDisco well they did play with a thing and then did some working out

[@ocng]

Wow. That's even more interesting than the regular format!

[@frozenbacon]

I love this. Building a contraption just to figure out why a toy does what it does because it interests you. This is the type of stuff a kid would do that for some reason tends to be discouraged when you get older for nothing other than the fact that you are "too old" for that nonsense.

[@toastghost2448]

certainly one of the best videos on youtube

[@LordPhobos6502]

that noise at the end is very satisfying!

[@zaggydog1]

This is so cool - I had my cambridge interview with Hugh Hunt in that very room, a couple of months after getting my calculator signed by Matt at a talk

[@asdfghyter]

These guys are so cute! A really enjoy watching them nerd out with each other.

[@5eurosenelsuelo]

I love to see you both together

[@Neme112]

It's a terrific formula. Tremendous.

[@the3nder1]

That last bit is so satisfying.

[@DesmondAltairEzio]

i did not expect a second video

[@milkywaykid3440]

Incredible!

[@pedrocrb123]

"the euler disk that I did a video on recently" RECENTLY? have you been taveling in speeds close to the speed of light?

[@pedrocrb123]

I mean, It's the internet, 5 months is 17 quadrillion (in base universe) years

[@jarodboyd72]

+Pedro Cardoso XD

[@chillbro1010]

This video could have been recorded 4 months and 29 days ago though, and only now uploaded. So at time of filming it was recent, but at time of posting it was not recently.

[@pedrocrb123]

indeed

[@1019wc1019]

that moment you think content is uploaded right after its filmed.

[@tylerburns8346]

Frickin awesome!!!

[@seanisawesome000]

This is so cool!

[@farpointgamingdirect]

Anyone else see the dunking bird in the background to the right? I love those things. Always something interesting to discover in Matt's videos. I wish I could get him to come to a convention I'm an owner of called Farpoint. He'd be a great science/technology/math guest!

[@jattprime2927]

i am as excited about matt's videos as matt is when meeting hugh

[@ShubhamBhushanCC]

DAYUM. This is the coolest thing ever

[@Quantiad]

Loved it.

[@shadowsp8888]

Love it!

[@Neppord]

More this was awesome! Gif more plix!

[@nandomax3]

This guy is super funny! I would love to have a teacher like him!

[@lawrence-dol]

Matt is awesome!

[@L4Vo5]

I seriously was at the edge of my seat with that race

[@benmcreynolds8581]

That is the coolest thing ever!!!

[@mixolydianmel]

Lovely 4x4 in the background

[@wildgoosechase4642]

Matt: This time, I have brought something Hugh: *tries to hold in a smile*

[@Garbaz]

Excellent ending !

[@ThIrDWatCher]

Two guys spinning their Euler Disks... this is nerdtastic! love it

[@sirgermaine]

Great Ending!

[@teachermichaelmaalim6103]

First time I have seen the Euler discs. I often spin cups and bottles but I never knew that the speed-up effect has a name. KZbin is better than university.

[@phampton6781]

I think you and Brady should introduce Hugh to Cliff Stoll. They'd get on like a house on fire, I feel. Could be the start of a new science KZbin duo in fact!

[@paxdriver]

Spinoff was the greatest thing I've seen on KZbin Lmao great job guys

[@TyphoidBryan]

"Epic Battles in Euler Disk History"

[@Ahmed-vk8pv]

I love this video! BTW, I noticed that here is the difference between maths and Engineering: 9:54 and 11:31 I personally prefer engineering but I realize that they both are beautiful in their own ways.

[@samuelcrouch8692]

Yup. A good video as always.

[@ImProvementSC2]

The race was oddly exciting!

[@NeonsStyleHD]

Love that final sound, like a little engine lol Another interesting thing on that you could see who was going to win, because there was a circle of light reflecting from both disks when the camera was equidistant from them, and Matts circle was larger than Hughs (higher angle) lol. Interesting experiment.

[@adamstoner3191]

11:33 - Matt reveals his inner Plato

[@ovekarlsson9881]

Is that Hugh Hunt or Mark Williams? Anyway, more from the pair of you, please. Most entertaining and educational.

[@bikingforbrie]

Is there an episode discussing what factors make an Euler Disk spin longer? I've wondered this since I was a little kid spinning coins.

[@elmohead]

Matt is most well-known for his ground-breaking work on parker squares.

[@chinareds54]

(1/cos theta)-1 would be a secant graph shifted down by 1 in the y axis. So it would start at (0,0) and curve upwards to infinity at 90 degrees

[@macazu75]

Magnifico..!!!

[@bevkcan]

I wonder how much air resistance affects the slow down. Vacuum chamber experiment maybe??

[@bevkcan]

+Adam Sowder I meant the regular euler disk, not this setup

[@santiagopicco1397]

Probably you lose more energy due to vibrations (sound) than due to air resistance.

[@bevkcan]

+Santiago Picco true, but in a vacuum chamber the only vibrating medium would be the mirror. Maybe it would result in better longevity. But one more complication occurs: how do we spin the disk in the first place? lol

[@Begviling]

the way hugh releases it is probably fairly easy to simulate with a sort of claw rig to drop it in a precise way

[@bevkcan]

+EffingTank yeah maybe

[@scythelord]

I have the exact same Euler disk that you guys raced with at the end and I spun mine at the same time as your race. Mine lasted about 27 seconds longer than either of yours.

[@Piffsnow]

Ahah ! I love how nerdy this channel can get ! :)

[@andrewaufderheide9852]

INTERVIEW IN PROGRESS PLEASE WAIT TO BE CALLED

[@hyatlnbimas6270]

When you said, you were djs I couldn't help but smile.

[@lookatdatcake245]

There is a Guinnes World Record certificate in the background! I would love to see a video on what Hugh got it for

[@jackwilliams7193]

The most stairs descended by a slinky is 30 and was achieved by Marty Jopson and Hugh Hunt (both UK) on The One Show in Cambridge, UK, on 18 February 2014.

[@beningram1811]

For measuring the angle on his air assisted rig, could it be filmed with a high speed camera and a series of angles marked in the background (similar to a protractor) and then choose the frame from the footage that has the plane of the disc perpendicular to the camera? That way you get a still image with the angle on it, and can get a more exact measurement than using the rubber finger thing and stopping when it looks close enough.

[@Somefurfag]

Thank you, Gyro.

[@draketungsten74]

Can't wait to see this done on the Moon!

[@nataliekanakova9496]

Matt is so cute, you can see pure happiness in his eyes throughout the video :)

[@jaypennebaker9979]

Ha! Disc jockey! That just made my night!

[@cameodamaneo]

10:28 This is one of the reasons we need formula sheets in exams at uni. Even good mathematicians like these two can't remember everything!

[@mathmachine4266]

Math Machine I did some maths. I assumed the disc is of uniform distribution, there's no rolling friction, and there's no air resistance. Under these conditions, I believe the disc should remain at a constant angle from the horizontal. The rate at which the disc spins around the vertical axis is equal to √(6g(2rcos(θ)-hsin(θ))/(sin(θ)((3r²+4h²)cos(θ)+6hrsin(θ)))), where h is the thickness of the disk. Assuming the height is small compared to the radius, this leads to a rotation speed of 2√(g/(rsin(θ))), and assuming θ is small, this gives your approximation of 2√(g/(rθ)). In addition, the rate of rotation of the dot placed on the disc is equal to the rotation speed around the vertical axis, multiplied by cos(θ). A small note, according to the formula I provided, the rate of rotation when θ=π is √(g/r). Technically, the disc could rotate at whatever speed it wants at this angle, as it's technically in equilibrium. However, if the angle were slightly below π, it would need to have a rotational speed of about √(g/R) in order for it to not fall into either the vertical position or towards the ground (depending on how stable the θ=π equilibrium is).

[@dl950]

Would the rate change if a disc made of a material with a higher coefficient of friction to metal was used?

[@deanofdeans]

Hey Matt, what about the diameter of the 2 circles, can you deduce the disks height and thus all the information like beta dot, theta, and omega

[@rishabhdhiman9422]

By far the best intro in KZbin.

[@Demasturbot]

Rishabh Dhiman Check out Despacito.

[@RyanKelley87]

I'd be interested to see how long a disc spins for a given angle. Will doubling the angle double the time of the spin? or is it analagous to how fidget spinners require exponentially more force to double the time they spin?

[@brianb2308]

I love the drinking bird on the right just chilling there for the whole video (except the experiment and zoom ins)

[@speedbump0619]

I've just discovered this channel, so I've probably missed my chance to ask the burning question: the CG of the disk is moving. If there were zero losses to friction, slippage, or air resistance, what path would the CG follow. Does the path that is actually followed provide a measure of the friction coeficient?

[@RealNovgorod]

Reminds me of good old times when I used to do that with heavy CF160 stainless-steel vacuum chamber flanges...

[@Rugg-qk4pl]

Was that the same university that vertasium did the weightless disk thing?

[@Vedvart1]

9:05 "I worked it out myself!" *Puffs out chest proudly*

[@TehDMBfan]

Do us all a favour and put these two guys on prime time tv

[@rajeev_kumar]

Good one

[@MrMontugar]

would sympathetic resonance in the table cause the two discs to couple over time?

[@longlostwraith5106]

For anyone interested, here's the graph of (1/cosθ - 1). prnt.sc/etil7y

[@winstonhwang7365]

The graph (drawn on the paper) was supposed to go from y=1 at x=0 to y=positive infinity at x=pi/2 if you're considering only 1/cosx where 0

[@stefanf922]

love it, now let's see the world's largest Euler's disk!

[@frankharr9466]

I'd forgotten about this.

[@iLikeKittens]

It's like watching young Matt & old Matt