this post was submitted on 01 Dec 2023
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[–] [email protected] 2 points 11 months ago (5 children)
[–] [email protected] 22 points 11 months ago (4 children)

if the path had been straight yeah, but the path itself rotates 360 degrees, which gives us an extra rotation

[–] [email protected] 8 points 11 months ago

This is the comment that finally enlightened me

[–] [email protected] 2 points 11 months ago
[–] [email protected] 2 points 11 months ago

This finally made it click. Thanks

[–] [email protected] 0 points 11 months ago

Now that is mind-bending trickery! Having a degree in applied matha millennia ago did not help...

[–] [email protected] 10 points 11 months ago* (last edited 11 months ago) (1 children)

That's what you'd think, but there's an extra rotation involved in the act of the small circle moving around the larger circle rather than along a straight line, so it's (6π/2π) + 1

[–] [email protected] 4 points 11 months ago* (last edited 11 months ago)

I just watched the video, that's really interesting. Thanks for the explanation

[–] [email protected] 6 points 11 months ago (2 children)

Watch the video, it's explained.

[–] [email protected] -2 points 11 months ago (2 children)

This should have been an article. What's the summary?

[–] [email protected] 1 points 11 months ago (1 children)

I summarized it above, there's an extra rotation included when the outer circle moves along the inner circle, essentially falling a bit with every roll forward. If the outer circle rolled along a straight line of the same length as the circumference of the inner circle, it would only roll 3 times, but moving around the circle instead adds exactly one extra rotation. That other gent says this is used in calculating orbits too, where you're also moving forward while constantly falling

[–] [email protected] 1 points 11 months ago (1 children)

I read an article about it. Everybody is doing a shit job of describing what happens. The outer circle naturally makes a full rotation as it travels around the inner one, as the path it follows goes around a full 360°, so that counts as one of the rotations it ends up making, which is in addition to the 3 due to travel around the circumference.

[–] [email protected] 2 points 11 months ago (1 children)

thank you, that was the comment that explained it for me

[–] [email protected] 1 points 11 months ago

Thanks for letting me know! It was too frustrating to not share.

[–] [email protected] -3 points 11 months ago* (last edited 11 months ago) (2 children)

Add the radius together. If the circle is inside. B-A 3-1 = 2.

[–] [email protected] 1 points 11 months ago (1 children)
[–] [email protected] -2 points 11 months ago* (last edited 11 months ago) (2 children)

It’s in the video.

A circle with a radius of 2 and a circle with a radius of 3 would be 5 rotations.

[–] [email protected] 3 points 11 months ago

First you said add the radii together, then you gave an example subtracting them, but either way this is incorrect. You divide the larger radius by the smaller radius and add 1

[–] [email protected] 1 points 11 months ago* (last edited 11 months ago)

Not quite. With radius 2 and 3 circles, the outer circle would take 2.5 rotations to complete the revolution. You have to set the first circle radius to 1 (divide both radii by the lesser) and then add the radii to calculate the relative circumference of the circle drawn by the motion of the center of the outer circle, so the answer would be calculated like:

2/2 + 3/2 = 5/2 = 2.5

[–] [email protected] 5 points 11 months ago

The center travels 2π per rotation but need to travel 8π because the path of the center of the small circle is a circle 4r the radius of the large circle plus the radius of the small circle. It would be three if the center of the small circle traveled along the edge of the larger circle but it's edge to edge.