Hoop stress of a rotating hollow hemisphere

[andelony]

Homework Statement

Hi all! I am an undergraduate who is currently doing a design on amusement ride. MY amusement ride would have a hollow hemisphere that is being rotated by a shaft. I need to determine the stresses acting on the hemisphere in order to know the material to use to build this structure. I do understand that all rotating bodies would encounter hoop and radial stresses. However, i only manage to find equations for rotating disk and cylinders. I cannot find any equaitons governing the rotation of a sphere, let alone the rotation of a hollow hemisphere. Therefore, I hope that i can get some help from you guys.

I did think of calculating the centrifugal force for the hemisphere, which is m*r*omega^2, and dividing this force by the area of the hemisphere, to which it is experiencing the hoop stress, ie (m*r*omega^2) / (pie*r1^2 - pie*r2^2), to get the hoop stress. r1 is the radius of the outer hemisphere, and r2 is the radius of the inner hemisphere. I would assume the radial stress to be negligible too. Is my approach correct? I would deeply appreciate it if anyone can enlighten me! Thanks alot.

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[jbsteele]

Moderator note: Please don't post multiple questions in the same thread. If you have a separate question, please start a new thread.]The Attempt at a Solution My approach is correct. The hoop stress acting on the hemisphere can be calculated by dividing the centrifugal force by the area of the hemisphere. The radial stress will be negligible due to the symmetry of the hemisphere.