The Maths of Spinning Coins and Euler's Disk

  • Published: 21 March 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:
    Here are the videos of the disk spinning:
    10% SPEED:
    Music by Howard Carter
    Design by Simon Wright
    MATT PARKER: Stand-up Mathematician
    Maths book:
    Nerdy maths toys:

Comments • 871

  • Kota Dagnino
    Kota Dagnino  13 ore fa

    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

    • Hayk and Arthur's channel

      I am 12 years old and I know that it’s wrong

      • po paipai
        po paipai  Mese fa

        I do not understand why we have to subtract the smaller circumference from the larger one, what does the difference between the two circumferences mean ? And why do we have to divide the difference between the two circumferences by the smaller circumference, what does the ratio mean ?

        • steven stallings
          steven stallings  Mese fa

          Precess. r^0/t^0=1 Velocity. r^1/t^1=v Acceleration. r^1/t^2=a a*v=Q = r^2/t^3 charge I = r^3/t^4 current O magnetism. r^3/t^5=O m mass. r^4/t^6=m Mass is a precess of current loops of charge Charge is unbalanced equllibrium of collapsing space time

          • YE E
            YE E  Mese fa

            What about the Energy calculations. Input VS output.

            • Billy File
              Billy File  Mese fa

              Is it not obvious that it has a 1/1 ratio.

              • Agus Busquets
                Agus Busquets  Mese fa

                this video was beyond amazing, the topic, the aesthetics, the editing, everything

                • ElektroMyth
                  ElektroMyth  2 mesi fa

                  After waking up from a lucid dream, I spun a penny and said, "the length of time this coin stays up is the length of that dream." The coin spun and spun and came to a stop, but it never fell down.

                  • the marble racer
                    the marble racer  2 mesi fa

                    I think there's only one group of people. Show us the spinning disk

                    • Ap0c
                      Ap0c  2 mesi fa

                      spin the damn thing already.!

                      • ehcmier
                        ehcmier  2 mesi fa

                        Euler's disc on a particularly large and polished steel drum.

                        • Fluffy Boi
                          Fluffy Boi  2 mesi fa

                          Disc sounds like car, not disappointed

                          • Elias N.
                            Elias N.  3 mesi fa

                            Pause the video at 5:10 right when Matt is saying the O in, "Wobble."

                            • Marcus Saastamoinen
                              Marcus Saastamoinen  3 mesi fa

                              my left ear hurts

                              • Spidery Things
                                Spidery Things  3 mesi fa

                                This is exactly the problem that helped get Richard Feynman excited about physics again, and as he worked on this problem, it led him to consider "spin" and electron rotation properties, which led him ultimately, to the work for which he won the Nobel prize! See this video, starting at about 20 min --

                                • FourthDerivative
                                  FourthDerivative  3 mesi fa

                                  "Some men aren't looking for anything logical, like mathematics. They can't be bought, bullied, reasoned or negotiated with. Some men just want to watch the disk spin down."

                                  • Ryan Schlimme
                                    Ryan Schlimme  4 mesi fa

                                    It is COSINE not caws 😂😂😂🤭🤭🤭

                                    • Jim Kirk
                                      Jim Kirk  4 mesi fa

                                      I just want to see it spin.

                                      • Eddeh 07
                                        Eddeh 07  4 mesi fa

                                        So simple. So good. Great video!

                                        • Mark Herbert
                                          Mark Herbert  5 mesi fa

                                          I see to remember reading in Feynman's books that he noticed this in spinning plates and it led him on to make some other significant discovery

                                          • BL Mathematricks
                                            BL Mathematricks  5 mesi fa

                                            Who else only focused on the coin and forgot the explanation by him on the left side?

                                            • Raj Tagore
                                              Raj Tagore  6 mesi fa

                                              i need to know the number of takes you took to get the timing right...

                                              • Lu Cho
                                                Lu Cho  6 mesi fa

                                                This type of of videos should GOOGLE Put in my recommendation..

                                                • Lu Cho
                                                  Lu Cho  6 mesi fa

                                                  Woow!!!! First time i use my both left - right side of brain.. Fabulous.

                                                  • Tyrane Lewis
                                                    Tyrane Lewis  6 mesi fa

                                                    the Arrow is on the wrong side of disk. that's the bottom side of disk per included instructions. the smoothed edge is the bottom of disk and the edge you should start your spin on.

                                                    • Bemused Indian
                                                      Bemused Indian  6 mesi fa


                                                      • Yseult Ceirw
                                                        Yseult Ceirw  7 mesi fa

                                                        So as the angle decreases and the rate increases, does that also mean r slowly approaches R? I'm guessing it stops spinning *just before* they're equal because physics aren't necessarily as perfect as math.

                                                        • William Nix
                                                          William Nix  7 mesi fa

                                                          I got this exact one, it freaks people out. Found mine here ===>

                                                          • Tone Seeker
                                                            Tone Seeker  8 mesi fa

                                                            Uhhh, oh... ok. I think I got it now. On second thought..

                                                            • MatthewTB
                                                              MatthewTB  8 mesi fa

                                                              I bought my cal 3 teacher one last semester. He was a good teacher

                                                              • earthdog1961
                                                                earthdog1961  8 mesi fa

                                                                Freaking awesome Brother Man

                                                                • Tyler Abshire
                                                                  Tyler Abshire  8 mesi fa

                                                                  I wish this guy was my high school math teacher! lol

                                                                  • Witaj Śmiertelniku
                                                                    Witaj Śmiertelniku  8 mesi fa

                                                                    This is sooo good!

                                                                    • nerdi loo
                                                                      nerdi loo  8 mesi fa

                                                                      breakdancing coins? gotta love it.

                                                                      • Murad Beybalaev
                                                                        Murad Beybalaev  9 mesi fa

                                                                        Nice audio channels usage.

                                                                        • Cubemaster
                                                                          Cubemaster  9 mesi fa

                                                                          Who else came here because you saw it on The Big Bang Theory?

                                                                          • anomaly P
                                                                            anomaly P  9 mesi fa

                                                                            Stupendously done

                                                                            • Chris Coghill
                                                                              Chris Coghill  9 mesi fa

                                                                              Was hoping to discover why spinning the disk on a concave surface makes it spin longer? Something to do with cycloids and least energy? And why is it called Euler's Disk?

                                                                              • Arturo José Gonzalez Alvarenga

                                                                                7:46 perfection.

                                                                                • Luis Ramirez
                                                                                  Luis Ramirez  9 mesi fa

                                                                                  4:41 best timing ever

                                                                                  • Aarone George
                                                                                    Aarone George  9 mesi fa

                                                                                    Amazing video

                                                                                    • XBLMastrodicasa
                                                                                      XBLMastrodicasa  9 mesi fa

                                                                                      Stupid question. Is the plate that the disk spins on required for the effect to work or is it for another purpose?

                                                                                      • keith click
                                                                                        keith click  9 mesi fa

                                                                                        what a beautiful sine wave made by that arrow

                                                                                        • I Eat Garbage
                                                                                          I Eat Garbage  10 mesi fa

                                                                                          “Supersized mega version” Supermega

                                                                                          • Beth Johnathan
                                                                                            Beth Johnathan  10 mesi fa

                                                                                            very very good !

                                                                                            • Sergio Ontiveros
                                                                                              Sergio Ontiveros  10 mesi fa

                                                                                              Youre a fuckin asshole for stopping it repeatedly-_-

                                                                                              • Serpentine | カゲキ

                                                                                                If you listen to the right speaker only... It's what I hear in class XD If anyone ever wanted to know what ADHD was like, bring them to this video and tell them to just put on the right speaker.

                                                                                                • Shiv A Joshi
                                                                                                  Shiv A Joshi  10 mesi fa

                                                                                                  Wobble and spinning RICHARD FYNMEN ALSO DID SOMETHING SIMILAR

                                                                                                  • SY
                                                                                                    SY  11 mesi fa

                                                                                                    Oddly, weirdly hypnotic....

                                                                                                    • InItForTheParking

                                                                                                      It would have been funny if you just interrupting it just before it finished.

                                                                                                      • Hariben Ben
                                                                                                        Hariben Ben  Anno fa

                                                                                                        If i only could give 2 "like".... Hell i would have given

                                                                                                        • Vaibhav Divakar
                                                                                                          Vaibhav Divakar  Anno fa

                                                                                                          Awesome timing 👍

                                                                                                          • Silence43
                                                                                                            Silence43  Anno fa

                                                                                                            I replayed it twice to watch both

                                                                                                            • TheMan4407
                                                                                                              TheMan4407  Anno fa

                                                                                                              Cool! What I wanna know is the frequency of rotation as a function of time of the disc.

                                                                                                              • Aurodeep Ray Ray
                                                                                                                Aurodeep Ray Ray  Anno fa

                                                                                                                Matt with that haircut reminds me of jim carrey ....(it's a compliment)

                                                                                                                • Venkatesh babu
                                                                                                                  Venkatesh babu  Anno fa

                                                                                                                  Gets the pictures going well with the sheet spinner.

                                                                                                                  • Venkatesh babu
                                                                                                                    Venkatesh babu  Anno fa

                                                                                                                    The leftover can be tossed to other disks. At factorial!!!..

                                                                                                                    • Venkatesh babu
                                                                                                                      Venkatesh babu  Anno fa

                                                                                                                      This is how sheets can hold other sheets at the brink of circular extension.

                                                                                                                      • John-Athan Crow
                                                                                                                        John-Athan Crow  Anno fa

                                                                                                                        The arrow turns like the stopwatch

                                                                                                                        • chimetimepaprika
                                                                                                                          chimetimepaprika  Anno fa

                                                                                                                          Hands down... Probably one of my favorite videos of all time.... Then again.... I say that every time

                                                                                                                          • Hans Jørgen Nilsen

                                                                                                                            Not much going on here. He is just defining the angel. Not giving the differential equation describing the rate of the angular change and taking in the friction due to the surface between the disc and the mirror and also the drag due to the air resistans.

                                                                                                                            • allen84
                                                                                                                              allen84  Anno fa

                                                                                                                              U forgot about friction but whatever

                                                                                                                              • yeremia frans
                                                                                                                                yeremia frans  Anno fa

                                                                                                                                3:12 IT SOUNDS LIKE A TIME BOMB!

                                                                                                                                • hihtitmamnan
                                                                                                                                  hihtitmamnan  Anno fa

                                                                                                                                  it's not "fitta", it's "theta"...

                                                                                                                                  • Electromorphous
                                                                                                                                    Electromorphous  Anno fa

                                                                                                                                    But you didn't tell why only Euler's disc spins for so long. How is it made?

                                                                                                                                    • Pheðtsi Couthai Ðvaarol

                                                                                                                                      Give me the frequency-time graph.

                                                                                                                                      • Anon Anon
                                                                                                                                        Anon Anon  Anno fa

                                                                                                                                        Yoooooo one of those eulers disks costs a whopping 120 bucks

                                                                                                                                        • Christos Georgiou

                                                                                                                                          Please define what you mean by wobbling (i.e what is one wobble)

                                                                                                                                          • Conspiracy TV
                                                                                                                                            Conspiracy TV  Anno fa

                                                                                                                                            great math

                                                                                                                                            • sharki11
                                                                                                                                              sharki11  Anno fa

                                                                                                                                              What does he mean by the left over/bonus bit? I dont get where that comes from or why we subtract

                                                                                                                                              • New England Chick

                                                                                                                                                Jim Carrey?

                                                                                                                                                • DarkRaven118666
                                                                                                                                                  DarkRaven118666  Anno fa

                                                                                                                                                  that was impressive timing

                                                                                                                                                  • Remco Hamersma
                                                                                                                                                    Remco Hamersma  Anno fa

                                                                                                                                                    Very nice

                                                                                                                                                    • Rich M
                                                                                                                                                      Rich M  Anno fa

                                                                                                                                                      You made this in 2016. But it is my fave of 2017!...and this seems like the same math as two neutron stars colliding.

                                                                                                                                                      • Cesar Rodriguez
                                                                                                                                                        Cesar Rodriguez  Anno fa

                                                                                                                                                        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

                                                                                                                                                        • Uncle Benis
                                                                                                                                                          Uncle Benis  Anno fa

                                                                                                                                                          Euler's di*k.

                                                                                                                                                          • Justin Tee
                                                                                                                                                            Justin Tee  Anno fa

                                                                                                                                                            Shave that head bruh