Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for sponsoring this video. Click here to start using LastPass: https://ve42.co/VeLP
Animations by Prof. Robert Ghrist: https://ve42.co/Ghrist

Want to know more about chaos theory and non-linear dynamical systems? Check out: https://ve42.co/chaos-math

Butterfly footage courtesy of Phil Torres and The Jungle Diaries: https://ve42.co/monarch
Solar system, 3-body and printout animations by Jonny Hyman
Some animations made with Universe Sandbox: https://universesandbox.com/
Special thanks to Prof. Mason Porter at UCLA who I interviewed for this video.

I have long wanted to make a video about chaos, ever since reading James Gleick’s fantastic book, Chaos. I hope this video gives an idea of phase space – a picture of dynamical systems in which each point completely represents the state of the system. For a pendulum, phase space is only 2-dimensional and you can get orbits (in the case of an undamped pendulum) or an inward spiral (in the case of a pendulum with friction). For the Lorenz equations we need three dimensions to show the phase space. The attractor you find for these equations is said to be strange and chaotic because there is no loop, only infinite curves that never intersect. This explains why the motion is so unpredictable – two different initial conditions that are very close together can end up arbitrarily far apart.

Music from https://epidemicsound.com “The Longest Rest” “A Sound Foundation” “Seaweed”

Why does shaken soda explode? Does ice melt first in fresh or salt water?
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This video features experiments that have been shown to me by science teachers over the years. Does ice melt fast in salt water or fresh water was an experiment introduced to me at the Utah Science Teachers’ conference. The ring of metal over a chain demo came from a teachers event in Florida. The idea shaking a carbonated drink increases pressure came from an email.

Special thanks to Petr Lebedev for building the pressure gauge.

Links to literature are below:
Victims of the pop bottle, by Ted Willhoft. New Scientist, 21 August 1986 p.28

Carbonation speculation
The Physics Teacher 30, 173 (1992); https://doi.org/10.1119/1.2343501

Agitation solution
The Physics Teacher 30, 325 (1992); https://doi.org/10.1119/1.2343556

Filmed by Cristian Carretero, Jordan Schnabel, Jonny Hyman, and Raquel Nuno

Music from https://epidemicsound.com “Seaweed” “Quietly Tense” “Mind Shift” “Observations”

Origami is inspiring a plethora of new engineering designs. Try yourself: https://ve42.co/Origami
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Huge thanks to:
Dr. Robert Lang https://langorigami.com
Prof. Larry Howell https://www.compliantmechanisms.byu.edu/

On first glance it’s surprising that origami — a centuries old art of folding paper to achieve particular aesthetics — is applicable to engineering. But upon closer consideration there are a lot of reasons methods developed for paper folding are also applicable to engineering: origami allows you to take a flat sheet of material and convert it to almost any shape only by folding. Plus for large flat structures, origami provides a way of shrinking dimensions while ensuring simply deployment – this is particularly useful for solar arrays in space applications. Furthermore, motions designed to take advantage of the flexibility of paper can also be used to form compliant mechanisms for engineering like the kaleidocycle. Since the principles of origami are scalable, mechanisms can also be dramatically miniaturized.

Some of the work shown is based upon work supported by the National Science Foundation and the Air Force Office of Scientific Research under Grant No. EFRI-ODISSEI-1240417. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Special thanks to Patreon supporters:
Alfred Wallace, Arjun Chakroborty, Bryan Baker, Chris Vargas, Chuck Lauer Vose, DALE HORNE, Donal Botkin, halyoav, James Knight, Jasper Xin, Joar Wandborg, Kevin Beavers, kkm, Leah Howard, Lyvann Ferrusca, Michael Krugman, Noel Braganza, Pindex, Ron Neal, Sam Lutfi, Stan Presolski, Tige Thorman

Edited by
Jonny Hyman, Isaac Frame, and Derek Muller

Music by
Jonny Hyman

Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem – this video offers an intuitive explanation.
Part of this video was sponsored by LastPass, click here to find out more: https://ve42.co/LP

References:
Prof. Terry Tao’s Math Overflow Explanation: https://ve42.co/Tao

The Twisting Tennis Racket
Ashbaugh, M.S., Chicone, C.C. & Cushman, R.H. J Dyn Diff Equat (1991) 3: 67. https://doi.org/10.1007/BF01049489

Janibekov’s effect and the laws of mechanics
Petrov, A.G. & Volodin, S.E. Dokl. Phys. (2013) 58: 349. https://doi.org/10.1134/S1028335813080041

Tumbling Asteroids
Prave et al. https://doi.org/10.1016/j.icarus.2004.07.021

The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods
SIAM J. Sci. Comput., 30(4), 2084–2112
E. Celledoni, F. Fassò, N. Säfström, and A. Zanna
https://doi.org/10.1137/070704393

Animations by Ivy Tello and Isaac Frame

Special thanks to people who discussed this video with me:
Astronaut Don Pettit
Henry Reich of MinutePhysics
Grant Sanderson of 3blue1brown
Vert Dider (Russian YouTube channel)

Below is a further discussion by Henry Reich that I think helps summarize why axes 1 and 3 are generally stable while axis 2 is not:

In general, you might imagine that because the object can rotate in a bunch of different directions, the components of energy and momentum could be free to change while keeping the total momentum constant.

However, in the case of axis 1, the kinetic energy is the highest possible for a given angular momentum, and in the case of axis 3, the kinetic energy is the lowest possible for a given angular momentum (which can be easily shown from conservation of energy and momentum equations, and is also fairly intuitive from the fact that kinetic energy is proportional to velocity squared, while momentum is proportional to velocity – so in the case of axis 1, the smaller masses will have to be spinning faster for a given momentum, and will thus have more energy, and vice versa for axis 3 where all the masses are spinning: the energy will be lowest). In fact, this is a strict inequality – if the energy is highest possible, there are no other possible combinations of momenta other than L2=L3=0, and vice versa for if the energy is the lowest possible.

Because of this, in the case of axis 1 the energy is so high that there simply aren’t any other possible combinations of angular momentum components L1, L2 and L3 – the object would have to lose energy in order to spin differently. And in the case of axis 3, the energy is so low that there likewise is no way for the object to be rotating other than purely around axis 3 – it would have to gain energy. However, there’s no such constraint for axis 2, since the energy is somewhere in between the min and max possible. This, together with the centrifugal effects, means that the components of momentum DO change.

A planet has been predicted to orbit the sun with a period of 10,000 years, a mass 5x that of Earth on a highly elliptical and inclined orbit. What evidence supports the existence of such a strange object at the edge of our solar system?

Huge thanks to:
Prof. Konstantin Batygin, Caltech
Prof. David Jewitt, UCLA

I had heard about Planet 9 for a long time but I wondered what sort of evidence could support the bold claim: a planet at the very limits of our ability to detect one, so far out that its period is over 60 times that of Neptune. The planet 9 hypothesis helps explain clustering of orbits of distant Kuiper belt objects. It also explains how some of these objects have highly inclined orbits – up to 90 degrees relative to the plane of the solar system. Some are orbiting in reverse. Plus their orbits are removed from the orbit of Neptune, the logical option for a body that could have ejected them out so far. The fact that the perihelion is so far out suggests another source of gravity was essential for their peculiar orbits.

Special Thanks to Patreon Supporters:
Alfred Wallace, Arjun Chakroborty, Bryan Baker, Chris Vargas, Chuck Lauer Vose, DALE HORNE, Donal Botkin, Eric Velazquez, halyoav, James Knight, Jasper Xin, Joar Wandborg, Kevin Beavers, kkm, Leah Howard, Lyvann Ferrusca, Michael Krugman, Mohammed Al Sahaf, Noel Braganza, Pindex, Ron Neal, Sam Lutfi, Stan Presolski, Tige Thorman

Music from http://epidemicsound.com “Observations – From Now On” “Magnified XY”

I used a nitrogen membrane and Stirling cryocooler to liquefy nitrogen out of the air. For this video I partnered with Starbucks to celebrate their Nitro Cold Brew. Order one here: https://starbucks.app.link/derekmuller

Making liquid nitrogen is hard – in fact up until 150 years ago scientists doubted whether it was even possible to liquefy nitrogen. In 1823, At the royal institution in London, Michael Faraday first produced liquid chlorine, kind of accidentally by putting it under high pressure. He similarly liquefied ammonia.

Borrowing a mixture from Thilorier in France, a combination of dry ice, snow and ether, he reached a temperature of -110C. By 1845 he used this mixture plus a hand pump to pressurize gases to liquefy all the known gases except six, which included oxygen and nitrogen. These became known as the “permanent” gases.

A French Physicist Aimé compressed oxygen and nitrogen in tanks and then lowered them into the ocean over 1.6km deep, where the pressure got up to 200 atmospheres. Still the gases didn’t liquefy.

Only at the end of 1877 were the first droplets of liquid oxygen and liquid nitrogen produced, by Cailletet in France. He first tried oxygen by compressing it up to 300 atmospheres, cooled to -30C, but that wasn’t even enough to liquefy oxygen. But when he suddenly released the pressure, the expanding gas cooled, he estimated to -200C and he saw a mist and then droplets slide down the walls of his vessel.

It’s amazing how far we’ve come in that now I can purchase a helium-based cryocooler. It compresses and expands the gas to absorb heat from the tip of the cold finger and eject it into the surroundings at ambient temperature.

The Mars Helicopter, Ingenuity aims to make the first powered flight on another planet when it takes off on Mars. It has now landed and safely checked in with the rover. It should detach and fly within the first 30-60 days of the mission. I learned a lot getting to visit the drone right before it was mounted on the rover at NASA Jet Propulsion Laboratory in Pasadena.

How do you fly in 1% of Earth’s atmosphere:
Have large rotors (they are 1.2m in diameter) and spin them very fast, around 2500 RPM (5x the speed of a helicopter on Earth).

Plus the aircraft has to be light:
The Mars helicopter weighs in at 1.8kg or around the same as a laptop. Every piece had to be stripped down for weight. Instead of using aerogel for insulation, the craft makes use of CO2 gaps between components. Even aerogel was too heavy!

One of the major challenges is surviving the Martian night:
Temperatures plunge to -80C to -100C so two thirds of the craft’s power is actually used to keep its electronics warm. Only one third is used for flying. The estimated flight time is 90 seconds.

The craft can’t be driven remotely, it will have to fly autonomously, using its own sensor suite to determine how to fly. The round trip 20 minute delay with Earth means steering the craft from mission control would be impossible.

Huge Thanks to Patreon Supporters:
Philipp Volgger, Chris Vargas, Ron Neal, Alfred Wallace, Colin Bellmore, Michael Krugman, James Knight, Donal Botkin, Sam Lutfi, Mohammed Al Sahaf, Kevin Beavers, Chuck Lauer Vose, Bryan Baker, James Wong, kkm, Manuel Zürcher, Tige Thorman, Jasper Xin, Leah Howard, Daniel Milum, Mathias Göransson, Stan Presolski, Lyvann Ferrusca, Arjun Chakroborty, June Kang, Listen Money Matters, Pindex, Joar Wandborg, DALE HORNE, Parker Linn, Roberto Rezende

Jonny Hyman was a legend in editing, animation, filming, and sound design for this video.

Electric cars are now ready to take over thanks to advances in battery technology and their inherent benefits: torque, handling, maintenance. This video was sponsored by BMW: https://www.bmwusa.com/

Full disclosure: I drive an #electric #car. I think electric cars are the future, not mainly because they’re better for the environment (which they are if you drive the car for any reasonable length of time) but because they are just better cars. The have better torque and acceleration, better handling, they’re more efficient, quieter, they don’t smell, they’re cheaper to run and best of all you never have to visit a gas station – this appeals to me. I never have to worry about being low on gas because every morning my car is charged and ready to go – just like my phone and laptop. And if you’re worried about range, don’t. Almost all trips can already be done in an electric car with modest battery pack. And fast chargers along the way make it possible to do longer road trips if necessary. You have to make rest stops anyway, just time them with the charging. And consider that battery tech is getting dramatically cheaper, smaller, lighter. All these reasons are why I see the #future of cars as electric.

Writing & Research
Derek Muller
Jonny Hyman
Matthew Shribman https://ve42.co/sciencebath

Editing, Animation, Audio, & Music:
Jonny Hyman

Camerawork:
Raquel Nuno
Jonny Hyman

1890s Music “National fantasie” by William Paris Chambers, archived in Library of Congress
#BMWUSA #NEXTGen #BMWPartner #ad

Apollo astronauts trained in nuclear bomb craters at the Nevada National Security Site. But why?Thanks Audible! Start listening with a 30-day trial and your first audiobook plus two Audible Originals free when you go to http://audible.com/veritasium or text veritasium to 500500

I found this story fascinating because in a way a nuclear bomb crater is more like a meteorite impact site than an impact site itself. Consider: Barringer Crater was claimed to be a meteorite impact site but geologists dismissed it as a volcanic formation. It was only after studying nuclear bomb craters and the minerals found there that geologists concluded the energy and pressures that created Barringer Crater were too high to be from volcanic activity and therefore must have formed from a meteorite impact.

Special Thanks to:
Nevada National Security Site
The National Atomic Testing Museum
Jonny Hyman and Verse: https://youtu.be/7bUUGzi-AAY
Active Galactic for footage of craters in Arizona: https://youtu.be/yhoooBpndog

Special thanks to Patreon supporters:
a human, Alfred Wallace, Arjun Chakroborty, Brent Stewart, Bryan Baker, Chris Vargas, Chuck Lauer Vose, Clip Tree, Coale Shifflett, Colin Bellmore, DALE HORNE, Daniel Milum, Donal Botkin, Eric Velazquez, Illya Nayshevsky, James Knight, James Wong, Jasper Xin, Joar Wandborg, Johnny, June Kang, Kevin Beavers, kkm, Leah Howard, Listen Money Matters, Lyvann Ferrusca, Manuel Zürcher, Mathias Göransson, Michael Bradley Wirz, Michael Krugman, Mohammed Al Sahaf, OddJosh, Philipp Volgger, Pindex, Roberto Rezende, Robin DeBank, Ron Neal, Sam Lutfi, Stan Presolski, Tige Thorman, Warrior8252

Filmed by Raquel Nuno
Story and Editing by Derek Muller and Jonny Hyman
Music and Animation by Jonny Hyman
Produced by Casey Rentz

Aerogels are the world’s lightest (least dense) solids. They are also excellent thermal insulators and have been used in numerous Mars missions and the Stardust comet particle-return mission. The focus of this video is silica aerogels, though graphene aerogels are now technically the lightest.

At one point Dr. Steven Jones literally held the Guinness World Record for making the lightest aerogel and therefore lightest solid. If you’re interested in learning more about aerogels, let me know in the comments as there is a potential trilogy in the works…

Huge thanks to Dr. Stephen Steiner and the crew at Aerogel Technologies. To find out more or buy your own aerogel sample, check out: http://www.aerogeltechnologies.com/

Thanks to Dr. Steven Jones and Dr. Mihail Petkov at NASA’s Jet Propulsion Laboratory

And thanks to FLIR for loaning us the awesome high definition thermal camera. The footage is amazing! https://www.flir.com

Special thanks to Patreon supporters:
Donal Botkin, Michael Krugman, Ron Neal, Stan Presolski, Terrance Shepherd, Penward Rhyme and everyone who provided feedback on an early draft of this video.

Filming by Raquel Nuno
Animations by Maria Raykova
Drawings by Mariel Solsberg

Music From http://epidemicsound.com “Seaweed” “Swagger Stagger”