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October 30th, 2019, 02:41 AM   #1
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Cylinder dimensions when rotated around its axis

It's been a while since I've done anything from high school geometry so if the answer is very obvious I wouldn't be surprised!

Basically if we have aa cylinder which is rotated around its y-axis as depicted below



I'm trying to understand x1/z2 is equal to x2/z2 - or rather whether longest dimension of the curved face (in whatever rotation) and shortest dimension of the circular face of the cylinder retain their relative size. If not, is there a way to find them in terms of other dimensions - if say x1, z1 and z2 are known

Also, as an extra question if we were to rotate that cylinder in some other arbitrary direction, would the longest dimension always be the diameter of the circular face?

Last edited by edrdoss; October 30th, 2019 at 02:50 AM.
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October 30th, 2019, 05:09 AM   #2
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Rotation of a line segment about an axis parallel to that line segment creates a cylindrical surface. The radius of that surface is independent of the length of the line segment.
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October 30th, 2019, 05:21 AM   #3
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Ah, you're talking about projections onto a plane (if you want to make it clearer to the mathematically minded).

As for x1/z1 and x2/z2, this ratio will not remain the same. Think about when the circular face is facing us. z = D, and x = 0. Now what about when we are looking at the side? x is at its maximum, but z = 0. You can actually predict these values very easily with sines and cosines, but I don't know if you have learned about those yet.

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Not directly related to your question, but I thought this was what you were asking at first, so I'll include it, why not? Regarding the longest dimension of the circular face: No matter how you rotate a circle in 3D, even if you rotate around multiple axes, it will look like an ellipse, and the major axis of the ellipse (the longest dimension, if you want) will be the same as the diameter of the circle. So the apparent lengths (projections) of the y-axis line segments are the same in both cases.
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Last edited by DarnItJimImAnEngineer; October 30th, 2019 at 05:28 AM. Reason: Misread the question initially
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