  The understanding of the evolution of early-type stars is tightly related to
that of the effects of rapid rotation. For massive stars, rapid rotation
combines with their strong radiation-driven wind. The aim of this paper is to
investigate two questions that are prerequisite to the study of the evolution
of massive rapidly rotating stars: (i) What is the critical angular velocity of
a star when radiative acceleration is significant in its atmosphere? (ii) How
do mass and angular momentum loss depend on the rotation rate? To investigate
fast rotation, which makes stars oblate, we used the 2D ESTER models and a
simplified approach, the $\omega$-model, which gives the latitudinal dependence
of the radiative flux in a centrifugally flattened radiative envelope. We find
that radiative acceleration only mildly influences the critical angular
velocity, at least for stars with masses lower than 40 Msun. We explain this
mild reduction of the critical angular velocity compared to the classical
Keplerian angular velocity by the combined effects of gravity darkening and a
reduced equatorial opacity that is due to the centrifugal acceleration. To
answer the second question, we first devised a model of the local surface mass
flux, which we calibrated with previously developed 1D models. The
discontinuity (the so-called bi-stability jump) included in the $\dot{M}-T_{\rm
eff}$ relation of 1D models means that the mass flux of a fast-rotating star is
controlled by either a single wind or a two-wind regime. Mass and angular
momentum losses are strong around the equator if the star is in the two-wind
regime. We also show that the difficulty of selecting massive stars that are
viewed pole-on makes detecting the discontinuity in the relation between mass
loss and effective temperature also quite challenging.
