Motion of the atmosphere: The atmosphere spins right along with the Earth. However, large scale north-south movement of air and water create significant Coreolis forces. The fancy way to say it is, in a rotating frame of reference ya gotta account for conservation of angular momentum.
Another way of looking at it is from a viewpoint directly above the north pole. A chunk of air at the equator will have an
angular momentum of Mass x Velocity x Radius. Now consider the same chunk of air after if flows up to the 60th parallel. Angular momentum = Theoretically unchanged = Same mass x Half the radius x Twice the velocity. This effect guides ocean streams and jetstreams. In reality the moving air smacks into the air that's already there, converting angular momentum into nifty vortexes & cyclones & stuff.
Basic atmospheric processes:
Consider a chunk of air at sea level. If the air drifts upward, the work to get that done comes from
adiabatic sorta-isentropic expansion of the air. In other words, air swaps internal energy for altitude. The internal energy comes from cooling and expansion. This is the primary cause of temperature variations in the troposphere and a main player in most weather patterns. See
lapse rate.
Evaporation soaking up heat and rain releasing heat is the other main player in weather patterns.
All this is driven by temperature differences created by the sun. However, human industrial waste heat has reached an astounding 1/100th of 1% of solar heating across the planet. Future generations will have to take that into account - if they're lucky.