= Centrifugal strain of a thin elastic hoop
{title2=$\Delta r/r\simeq\rho\omega^2r^2/E$}
A small arc of a rotating thin hoop needs inward <force> per length $\rho A\omega^2r$. Its circumferential <tension> supplies this through curvature, giving <tension> $\rho A\omega^2r^2$ and tensile <stress> $\rho\omega^2r^2$. <Hooke's law> converts that <stress> to circumferential <strain>, which equals fractional radius change. Small <strain>, a slender cross-section and uniaxial <linear elasticity> are required; the cross-sectional area cancels at leading order.
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