  It has been proposed recently that the first step in the formation of both
rocky and gas giant planets is dust sedimentation into a solid core inside a
gas clump (giant planet embryo). The clumps are then assumed to migrate closer
to the star where their metal poor envelopes are sheared away by the tidal
forces or by an irradiation-driven mass loss. We consider the implications of
this hypothesis for natal rotation rates of both terrestrial and gas giant
planets. It is found that both types of planets may rotate near their break up
angular frequencies at birth. The direction of the spin should coincide with
that of the parent disc and the star, except in cases of embryos that had close
interactions or mergers with other embryos in the past. Furthermore, the large
repository of specific angular momentum at birth also allows formation of close
binary rocky planets inside the same embryos. We compare these predictions with
rotation rates of planets in the Solar System and also question whether the
Earth-Moon pair could have been formed within the same giant planet embryo.
