The most interesting thing about the teacups is the motion. From the outside looking in, a tripod is nice so that you can get long exposures of moving teacups. From the inside, exposures in the 1/30 to 1/90 range are nice. Done well, your subject will be sharp (people in the cup aren't moving relative to you) while the background will have a motion blur to it.
It is dark inside the ride area. During the day, using a flash is a must or the background will be blown out.