It finally occurred to me to look up the equations for stress in a rotating disk instead of trying to work them out myself, which I’ve obviously been out of college too long to be able to do anymore. Of course I found them, along with evidence that I’d looked for them previously, which is odd but irrelevant.

Short course in mechanics of materials: you apply force to a material, it deforms (bends, stretches, whatever). This leads to internal forces in the material, which we call stress. The amount of stress depends on the cross-sectional area of the material in the direction of the force. Any material can only take a certain amount of stress before it breaks.

So, the general idea is to figure out how much force you want to put on an object, and then figure out how beefy you have to make it so it can survive the resulting stress. That’s called engineering.

Anyhoo. These equations I’ve got have variables for material density, rotational speed, and more radii than you can shake a slide rule at. There’s one for stress in the radial direction, and one for the tangential direction. It all makes prefect sense.

Except there’s no thickness variable. There’s an assumption that thickness is much less than diameter, which means you don’t have to worry about stress on the surface versus stress in the center. But according to these equations, it doesn’t matter how thick the disk is; 1/16″ or 1″, the stress will be the same, if the diameter is relatively huge.

Which makes sense for a rotating disk. If it’s thicker, then the new material is also rotating and having to deal with its own stuff, so it can’t help reduce the overall stress level in the way that making a column thicker would help hold up the building better.

Which means this does me no good in determining how thick I need to make my disks. Or, looked at the other way, I can make them as thin as I want as long as they’re still stiff enough not to flutter in the breeze.

Oh, I never told you why I want rotating disks, did I? Hmm, weird.

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