A flywheel for energy storage is modeled as a rotating thin-walled cylindrical ring (t ≪ r) as shown in Figure 1.7. Find the equation for the tensile stress in the ring as a function of the mean radius, r, the rotational speed, ω, and the mass density, ρ, of the ring, then compare the maximum peripheral speed (tangential velocity) and the kinetic energy stored per unit mass of a ring made from 4340 steel with that of a ring made from IM-7 carbon fibers.
For the carbon fiber ring, assume that the fibers are oriented in the circumferential direction, and that the entire tensile load is supported by the fibers.

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FIGURE 1.7 00 L