This paper describes the application of Laser Doppler Vibrometry to vibration measurements on rotating targets. The noise generating mechanism of the laser speckle phenomenon is first explained before confirmation of the insensitivity of measurements to target shape. The principal focus of the paper is on the fundamental limitation associated with the use of Laser Vibrometers for radial vibration measurements directly on rotating components. In such measurements significant cross-sensitivities to speed fluctuations, including torsional vibrations, and in-plane vibrations are evident, preventing synchronous vibration analysis. Mathematical and electronic means to resolve the correct orthogonal vibration components are presented and shown to be successful in enabling the use of Laser Vibrometry for non-synchronous vibration measurements.