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Since you want the animation to have explanatory content, I thought it might be best to incorporate the explanatory 2D diagram into the 3D scene. So I imagine the 2D plot as a "sticker" that can be put onto the cylinder, like a label on a bottle. That way, you can see the explanatory diagram itself wrap around the cylinder and become identical to the ...


Show[ Graphics3D[Cylinder[{{0, 0, 0}, {0, 0, 12}}, 2/π]], ParametricPlot3D[ 2/π {Cos[θ], Sin[θ], 3 θ/4}, {θ, 0, 8 π} , PlotStyle -> Red]]

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