The first is called Doodling in Math Class: Snakes and Graphs. This amazing video is by Vi Hart, and she shows how to sketch elaborate doodles that have a mathematical theme. The very clever (and funny) commentary provides tip on how to draw, plus some hints about the mathematics that are associated with each sketch.
The second is a 50 minute video by Astronaut Don Petit, who recorded several of the fluid-dynamics experiments that he performed while in the microgravity environment of the Space Station; see this youtube video. One interesting clip shows an air bubble that he creates inside a floating water bubble, which to me resembles a miniature planet that has a central core and an overlying mantle. He then injects little water bubbles into the air core, which careen around and around the core boundary until getting absorbed explosively by the mantle. Another video segment show how small bodies in the weightless environment of space can collide, merge, and form elaborate dendritic objects. This is in fact how planetesimals, which are the precursors to asteroids and planets, are thought to have formed. A fascinating video.
The next two videos are from the Slo Mo Guys. They use a high-speed camera to record ordinary events that are usually just a blur. Playing their movies very slowly then reveals lots of hidden events that are too fast to be seen by human eyes. In the first video, Giant 6ft Water Balloon, one of the Slo Mo guys leaps onto and breaks a large water-filled balloon. Slow motion video reveals how the entire balloon shivers as inertial waves propagate across the balloon and ultimately rip the balloon to shreds. In very cool slow mo.
But my favorite movie is Droplet Collisions at 5000fps, which provides an excellent analogy for how craters form and develop when an asteroid impacts a planet. Oh, and the Slo Mo guys are hilarious, too.
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