How do you analyze stresses in a rotating disk and what limits rotational speed?

Rotating disk stresses arise from centrifugal forces: σr and σθ vary with radius according to Lame-type equations including ω²ρr² terms. For uniform disk, maximum stress occurs at center. For disks with central holes, maximum hoop stress occurs at the inner edge and equals 3+ times the average. Burst speed occurs when maximum stress reaches UTS. Gas turbine and flywheel design requires careful stress analysis with material and temperature variation through thickness.