A model is presented for the self-consistent interpretation of the global momentum and energy confinement times and the central rotation velocities measured in plasmas that are rotating at speeds comparable to their thermal speed. This model incorporates corrections for non-steady state and represents the effect of radial density, temperature and velocity profiles. The momentum transport model is based upon gyroviscosity theory, which remains controversial. Good agreement between measured and predicted rotation frequencies and momentum confinement times is obtained for a collection of JET data and for one TFTR beam power scan. The energy confinement is shown to be degraded by a viscous energy flux, which is predicted to account for up to one fourth of the total energy loss for the JET data and for one half of the energy confinement degradation measured in the TFTR beam power scan. This implies that the measured energy confinement times in strongly rotating plasmas are significantly shorter than the times of energy confinement against conductive and convective transport processes.