How is the atmosphere of a planet affected by the rotation rate?

A faster rotation rate produces stronger winds. This is the same reason that you have to spin a bottle very fast to create a whirlpool in the liquid. This is a good visual tactic to see how rotation rate affects winds; the swirling water acts as the air in the atmosphere. While winds typically go straight through, the water trick is a cool way to see how the stronger winds affect tornadoes specifically. All you need is a two-liter plastic bottle and some water. This will give you the clearest picture.

All the fun science experimentation aside, a faster rotation rate will also allow the planet to decay faster. Part of the reason is that winds can tear down trees and other vegetation that keep soil or the equivalent in place.