The Maths of Spinning Coins and Euler's Disk

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:

Music by Howard Carter
Design by Simon Wright

MATT PARKER: Stand-up Mathematician

[proefslak]

now THAT is what I call creative use of video.

[SinZ]

This video helped me find out that my left speaker wasn't working!

[sungahn]

I really appreciate that perfect timing of the wobble and the explanation. Well played, good sir.

[starwarsjk]

I did not expect the wobble to last the explanation.

[sean]

"some of you just want to want to watch the disc spin all the way down" I cracked up, exactly me

[RealBenAnderson]

There's a third group of people: those of us who just like watching you explain shit.

[Spiderelectron]

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.

[imeredithc]

It's crazy how the motion looks so complicated but it's described by a pretty simple relationship. Awesome video!

[markojelegenda]

4:44 was the moment i realized this is the most awesome video i watched in my whole life

[rickipedia]

I honestly expected you to finish the math early and grab the disc. It made it so much more satisfying when it finally stopped.

[marcoantonio]

The most amazing thing is how much I learned with only 8 minutes of video.

[Jotakumon]

That's one hell of a creative video. Fantastic. Hard to see something that is that so thought out and well timed on YouTube. 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.

[alfonshomac]

YAAAASSS!! <- at how cool it was when he finished explaining the maths and then calmly signals the coin to stop as if it was waiting for his command

[JishuSharma]

Nice video! The best part is that by the time it stops wobbling, you finish your calculation! Great timing!

[JupitersDancer]

4:44 You felt like a rockstar for second didn't you ? :D

[Rubafix]

You forgot the part of people that just wonder what the fuck they've been watching that late at night for the past hour. Count me in

[Yossus]

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.

[fisikalectures]

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

[DrDherp]

Man I was on the edge of my seat. Way to make maths dramatic. Also excellent choice in music.

[Holobrine]

That moment when you realize the traced circle is a section of a sphere with the same radius and center as the disc. 😳💥