The mysterious isochronous curve

[Music] yeah when you go riding your bicycle it's wheels describe isochronous curves what does that mean well imagine you have a piece of white paint on your black tire it'll come around hit the road stay stationary for a bit then come up over and around and hit the road and in doing that it describes an isochronous curve and it's a very interesting cure with very interesting properties I'll show you what first of all it's very hard to capture one off a bicycle so what we have to do is to at home create the same sort of conditions for drawing one first of all a roadway which you make out of a ruler and we will kept to the curve on a piece of paper everything has to be kept very very stable so stick the whole lot down sticky tape everywhere on the corners of the paper and across the ruler and that way we can't budge the ruler even with a favorite of pressure and the bike tyre is going to be provided by this wall the wheel is going to be at in this is a tobacco tin with a smooth lead not a serrated one and to stop it skidding on the ruler your roadway I've put on its own bike tyre that's a piece of already a whole rubber band which runs around there without any kinks and without any twists so it runs along the ruler doesn't skid and the whole thing rolls very smoothly but it doesn't leave a mark it doesn't for the isochronous curve so to do that you have to cut the point off a piece of or an old pencil sharpen it to a point and just slide that underneath the rubber band so that the point comes out below the tin lid and will rest on the piece of paper like that you have to stop at being pushed backwards and of course sticky tapes the answer there lots of it but don't did it muck up the rubber band couple another one on there just to make sure so that should hold the pencil in place the rubber band should stop the thing from skidding on the ruler and we're ready to draw it put it down with that pencil point right next to the ruler in that position there it's resting on the ruler hold the whole thing steady push the rubber band up against the ruler and rotate it the way your back wheel would roll along the road very slow here but that gives you can and while you do that the pencil point comes around and if you don't skid will describe a very smooth and beautiful I said Cronus curve there it is now you can just cut that out what I did was to trace it onto a piece of acetate that sort of thing that use in schools and projected onto a large piece of cardboard so you can see what's going on I've cut that out here it's rather special cardboard in that it's got hard cardboard on either side of a piece of foam and those are now going to act like tram rails so I can take a ball bearing and putting it on there it'll run between those rails up and down the curve and in fact it's the way balls run on that curve let's give it the name of isochronous because isochronous means same time and it's a very peculiar curve because if I let a ball go from any spot here and any spot here now both meet at the midpoint that red arrow at exactly the same time no matter where I release eyes are open oh sure yeah one two three click and they meet at the error other cures don't do that if we had a circle there or a fraction of a circle if I let one ball go there one ball go there that means somewhere here and if I put one there when they meet somewhere there they meet at different places but wherever we let these go on other sides of that they'll meet if we let them go at the same time at the red point click like that and one last time I'll either go near the middle here and up on the side here one two three click allowing for slight inaccuracies in manufacture that's not all it does you'd think that if we let a ball go up at the top here because it's got a very long way to go around that curve it would take longer to get to that point then if it took a straight line but that's not so either if I put the straight line in it's another piece of track I'll just make sure intersects it then red arrow and I put a finishing line there in the form of a match cross like that now if I come round here and release these two balls at exactly the same point one two three go and in fact the curve winds by quite a distance those are just a couple of the very peculiar properties of this most interesting isochronous curve [Music]

Channel: CuriosityShow

Views: 4,701,397

Rating: 4.8793349 out of 5

Keywords: Curiosity Show, Curiousity Show, Deane Hutton, science, Rob Morrison, Australia, Myth, Mythbusters, how to, education, isochronous curve, isochronous, geometry, physics, STEM, rolling ball, Make and do, gravity, physics pf gravity, momentum

Id: eBc827pwKf0

Length: 4min 39sec (279 seconds)

Published: Thu Jan 18 2018

Reddit Comments

[u/Boo_R4dley]

I miss the days when you could use a rusty tin of pipe tobacco in children’s programming and no one would bat an eye.

[u/Silvaski]

This guy is the Bob Ross of science, I want more, so relaxing and informative. Thanks for sharing.

[u/RiffRaff14]

Using foam core was a great idea. Easy way to get a ball bearing track without cutting out two pieces.

[u/Menospan]

https://youtu.be/skvnj67YGmw?t=8m28s

[u/printergumlight]

What are the applications/uses of the knowledge of isochronous curves?

[u/Sm0keydbear]

Vsauce did a video on this as well, although he called it a "brachistochrone."

https://www.youtube.com/watch?v=skvnj67YGmw

[u/TheRedGerund]

I can barely stand the high pitched sound in this video

[u/BubiBalboa]

Damn talk about nostalgia. I didn't even remember watching this show as a kid but I just got major fash backs into my childhood. Always enjoyed this program.

[u/hrfhrf]

Curiosity Show!!! Fuck I loved that! I still live about 500 metres from where it was filmed. Best after school watching ever.