Final answer:
A rotating spherical gas cloud collapses into a flat rotating disk due to the conservation of angular momentum. As the cloud collapses and spins faster, non-circular motions cancel out, favoring the formation of a flat disk, which leads to planets orbiting in the same direction.
Step-by-step explanation:
A rotating spherical gas cloud collapses into a flat rotating disk primarily because of the conservation of angular momentum, which is a fundamental principle in physics. The initial rotation of the gas cloud meant that as it collapsed under gravity, the rotation rate increased. At the same time, particles moving in non-circular orbits collided, and their motions tended to cancel out, except for the motion in the plane of rotation, reinforcing the disk shape. This effect is similar to how a figure skater pulls her arms in to spin faster; as the nebula contracts, it spins more quickly, with faster-moving material forming a flat disk around the central object. This forming disk is the precursor to a planetary system where all planets orbit in the same direction due to this conserved angular momentum.