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You can see the strength in paper simply by rolling it up into a cylinder and aplying pressure to the open cylinder ends. The paper can take quite a lot of pressure before it folds. So basically I think you hit upon the intrinsic property that is necisary for this physics project. You proly could have done the same with a square shaft, but it would have used more paper. Using a cylindrical shaft is both efficient and strong. Same way tube steel is used for roll cages in race cars. Strong yet light.
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