Talks at Google cover image

Ep417 - Matt Parker | Things to Make and Do in the Fourth Dimension

Talks at Google

CHAPTER

Exploring the Motion of Rolling Discs

Exploring the unique motion of a circle rolling and maintaining the same level of its center of mass, demonstrated through intersecting discs and calculations using Pythagoras and similar triangles.

00:00
Speaker 1
So, a circle rolls because as it rotates the center of mass days, it'll be like in the same height, very, very handy, but if you get two discs and you intersect them like this at right angles, and I made those notches, so the centers of the two discs are now root two apart compared to the radius. So, if you've got one unit as the radius, that's root two, the distance between the two discs, and what it means is as this rotates on a flat surface, the center of mass stays at exactly the same level, and I haven't got a flat surface here. I'm going to try it over here. I checked my cables not long enough to get the camera over there, but I'm going to try it on this bench if you don't mind. So, if I put it there, if I give that a bump, the center of mass stays at exactly the same height. If you want to kick that back in the opposite direction, it's optional. Feel free to join in on that. So, the center of mass is going side to side. It's not even a sign that, going back and forth, it's quite a complicated wave. It's a combination of different curves, but in terms of its height above the surface, it stays perfectly flat. And you can prove that for two main locations using nothing more complicated than Pythagoras or similar triangles. So, that's your challenge for when you should be working. Use some of your 10% time to calculate why the center of mass. Because what you do is assume the center of mass stays at the same height, and it will drop out that the center of the disc has to be root two apart. It's the easiest way to go about it. And using Pythagoras and similar triangles, you can show that. I will leave it up there. And if you want to have a play with it afterwards, you can roll it backwards and forwards on there. Or you can make your own CDs, which you might have in some of the display cases with technology from the past. So, all make your own circles. You can get those to roll quite nicely. It's kind of fun.

Get the Snipd
podcast app

Unlock the knowledge in podcasts with the podcast player of the future.
App store bannerPlay store banner

AI-powered
podcast player

Listen to all your favourite podcasts with AI-powered features

AI-powered
podcast player

Listen to all your favourite podcasts with AI-powered features

Discover
highlights

Listen to the best highlights from the podcasts you love and dive into the full episode

Discover
highlights

Listen to the best highlights from the podcasts you love and dive into the full episode

Save any
moment

Hear something you like? Tap your headphones to save it with AI-generated key takeaways

Save any
moment

Hear something you like? Tap your headphones to save it with AI-generated key takeaways

Share
& Export

Send highlights to Twitter, WhatsApp or export them to Notion, Readwise & more

Share
& Export

Send highlights to Twitter, WhatsApp or export them to Notion, Readwise & more

AI-powered
podcast player

Listen to all your favourite podcasts with AI-powered features

AI-powered
podcast player

Listen to all your favourite podcasts with AI-powered features

Discover
highlights

Listen to the best highlights from the podcasts you love and dive into the full episode

Discover
highlights

Listen to the best highlights from the podcasts you love and dive into the full episode