I don't think it really has anything to do with the shape of the cloud. The force of gravity can be simplified to a single point mass acting at a certain distance, regardless of the size or shape of the mass. The main thing that would matter is the size/shape of the object being pulled by this gravity and how much the gravitational force changes over its mass. In most cases the center of gravity will be the same or very close to the center of mass, and thus no spinning would be induced. The only cases where this wouldn't be true is if the object is extremely long or it is in a very strong gravitational field such as near a black hole where the forces change enough to create a center of gravity far from the center of mass. However, even in a case like this, the object would essentially turn into a pendulum, not a spinning ball. The center of gravity of the smaller object being moved would try to align itself with a line intersecting the centers of mass of the interacting objects (because with that orientation there would be no moment formed). So if you had a long rod, it would essentially want to point toward the equivalent point mass where it felt the force of gravity. This would cause the rod to start rotating toward that orientation, but as soon as it passed that orientation, it would be pulled back, thus creating a pendulum motion; not a full spinning motion.Are you claiming that the gravity of such a cloud is so perfectly spherical that there would be no tidal effects on any part of the cloud?
As I just explained above, the spinning would most likely be a pendulum motion rather than the rotation of the planets we see. It would still be possible to get the full rotation if the masses moved in the perfect way to get something moving toward a specific orientation, and then moved far enough out of the way to be unable to reorient it. Regardless, a cloud of dust would not create the conditions for centers of gravity to be very far from the centers of mass of objects. The cloud is huge and not very dense, so obviously the forces of gravity would not change greatly with distance nor would the gas be large, continuous objects like a rod. So induced spinning would be very small, if any.To claim that no differential gravity ever acted anywhere to start things spinning (in various different directions across the universe, averaging to zero) is an extremely extravagant and improbable claim, but that appears to be the claim you are making. You might want to stop and think.
Almost all the planets, stars, moons, and asteroids/meteors are spherical or round. They were created by gravitational forces, so it seems to be the natural formation. However, mathematically, since all points on the surface of a sphere would be at the same gravitational potential, there would be more of an equilibrium than other shapes, such as a rod (and since everything tends toward an equilibrium, the sphere would be the natural tendency). Objects would be attracted to the center of mass (to go toward the least gravitational potential), so on a sphere, there are no points that would have lower gravitational potential than another (except if there were different elevations such as a mountain, but that's why things will roll down). On a rod, things would want to roll toward the center, making it even itself out over time so that there was no specific point to which mass would "fall" toward, and hence create a sphere eventually.Why? Why would a mass distribution that doesn't start out as spherically symmetric, become spherically symmetric because of gravity?
Then what kind of motion is it? For one, big bang sounds like an explosion. For another, it started out as a singularity and expanded outward. If it started out as a point, there's not much else it can do besides radiate outward. And I'm not saying they can't have angular momentum. I am asking how they actually got it in the first place.This is completely wrong. The big bang was not an explosion and the expansion of the universe is not like normal radial motion. In any case, as Peter has already said, individual parcels of gas (or plasma in this case, see below) can have net angular momentum even though the whole universe has no net angular momentum.
I'm not sure how a spin would arise from these variations in density. I'll have to think about that.That is indeed the case. The spin arises from variations in the density of the hot, dense plasma that filled the very early universe.