Distance round a circle
Discussion
Ok usually I'm quite good at things like this and I'm the one who ends up explaining things to other people when they are convinced its black magic but this one has me a bit stumped and its probably primary school engineering really.
The beginning bit of this video where he is rolling the wheel along a linear surface and then around a wheel.
I get that the centre of the wheel is travelling the same distance along its length when its a flat surface but it has to travel a lot farther when its going round in a circle so the wheel has to rotate twice to cover that greater distance but.... how does the tyre know its going round in a circle and not along a flat track, it has traction on the surface and the outer edge is traveling along the exact same length but it isn't skidding along to do the extra rotation.
The only thing I can think of is because the surface is now curved then there is less contact area so it has to do more revolutions but that could be well wide of the mark for all I know. I just can't get my head round this for now.
The beginning bit of this video where he is rolling the wheel along a linear surface and then around a wheel.
I get that the centre of the wheel is travelling the same distance along its length when its a flat surface but it has to travel a lot farther when its going round in a circle so the wheel has to rotate twice to cover that greater distance but.... how does the tyre know its going round in a circle and not along a flat track, it has traction on the surface and the outer edge is traveling along the exact same length but it isn't skidding along to do the extra rotation.
The only thing I can think of is because the surface is now curved then there is less contact area so it has to do more revolutions but that could be well wide of the mark for all I know. I just can't get my head round this for now.
It's an interesting one, did my head in at first just like yourself. The explanation for the centre of the wheel seems quite straightforward, until you think about it like you say!
His explanation of the teeth and gears helps I think. Imagine one tooth on the round gear running along the straight gear, the round gear has to turn a certain amount for the given tooth to reach the next tooth on the straight gear. Take the same tooth on the round gear, but now moving around the big circular gear. The tooth doesn't just have to travel 'right a bit' like it did for the straight gear, it also has to travel 'down a bit'. That 'across a bit and down a bit' is further to travel, which I think accounts for the difference. At least that's how I can get it to make sense in my head.
His explanation of the teeth and gears helps I think. Imagine one tooth on the round gear running along the straight gear, the round gear has to turn a certain amount for the given tooth to reach the next tooth on the straight gear. Take the same tooth on the round gear, but now moving around the big circular gear. The tooth doesn't just have to travel 'right a bit' like it did for the straight gear, it also has to travel 'down a bit'. That 'across a bit and down a bit' is further to travel, which I think accounts for the difference. At least that's how I can get it to make sense in my head.
Replace 'wheels' with 'circles on paper'.
Draw 2 circles touching at the perimeter. Stick the point of a compass through the centre (axis) of the fixed circle, and the pencil through the centre (axis) of the moving one. Draw that circle, and while you're there draw a straight line between the two axes. You'll notice that straight line is just the radius of the first circle, and the radius of the second circle.
Double the radius, you get double the circumference. From the first example, 1 rotation = 1 circumference of distance traveled. So if the circumference is doubled, double the rotations are needed.
Draw 2 circles touching at the perimeter. Stick the point of a compass through the centre (axis) of the fixed circle, and the pencil through the centre (axis) of the moving one. Draw that circle, and while you're there draw a straight line between the two axes. You'll notice that straight line is just the radius of the first circle, and the radius of the second circle.
Double the radius, you get double the circumference. From the first example, 1 rotation = 1 circumference of distance traveled. So if the circumference is doubled, double the rotations are needed.
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