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The Jones calculus is used to describe the frequency shift 2 ω suffered by circularly polarized light as it passes through a half-wave retardation plate rotating with angular velocity ω. The phenomenon is also explained in terms of an angular Doppler effect and is related to the quantum of angular momentum carried by circularly polarized photons. Experimental demonstration of the effect is reported using a HeNe laser beam at 633 nm. Rotation-induced optical activity is also discussed.