  I show the existence of a new type of vortex solution which is non-static but
stationary and carries angular momentum. This {\it spinning vortex} can be
embedded in models with trivial vacuum topology like a model with
$SU(2)_{global}\times U(1)_{local} \rightarrow U(1)_{global}$ symmetry
breaking. The stability properties of the embedded spinning vortex are also
studied in detail and it is shown that stability improves drastically as
angular momentum increases. The implications of this result for vortices
embedded in the standard electroweak model are under study.
