Previous Space-based experiments (Wang et al.
1994a) showed that a rotating liquid
drop bifurcates into a two-lobed shape at a lower critical angular
velocity, if it is
flattened acoustically by the leviating sound field. In this work,
we undertake a
systematic experimental study of the effect of acoustic flattening
on the rotational
bifurcation of a liquid drop. We also look into the complementary
effect of rotation on
the equilibrium of an acoustically drastically flattened drop.
Theoretical models are
developed for each of the two effects and then woven into a
unified picture. The first
effect concerns neutral equilibrium, while the second concerns
loss of equilibrium,
neither of them involving instability. The theories agree well
with the experiments.