Liseberg has long physics traditions - Einstein gave a talk in Liseberg in 1923, which is also the year the park opened.
For a sample of amusement park science, take the main entrance and continue until you reach the Rabbit river ride. Turn left after the rabbits, just before the children's roller coaster. The "Circus Express" is the only roller coaster running in winter (and only down to about -5oC); with the cold, the energy loss in the wheels is too large, and the trains in the large roller coasters may not make it back to the station. If you look carefully, you can see that the little train is warmed up at the station.
Just after the Circus Express, you come to a carousel with swings, "Slänggungan". If you are lucky, it starts half-loaded, and you can watch how the empty and loaded swings always make the same angle to the vertical. The equivalence principle in front of you eyes! And you might like to recall Eötvös who used the spinning earth as a giant carousel to test the equivalence principle.
The coffee table "Kaffekoppen" just after "Slänggungan" combines a clockwise motion of the table with a faster counter-clockwise motion of the three trays (and also the cups can be turned by the passengers). The combined motion for someone on the ride depends on the ratio between the angular velocities for the rotations, which varies between different versions of the attraction (a nice introductory programming exercise!). In Liseberg's case, the rider follows a starshaped motion.
The classical merry-go-round with horses and elephants is Liseberg's oldest attraction - it has been around since 1923. It is slow enough that a miniature Foucault pendulum experiment can be fun. (It is even better in the high tower, that is now a Christmas tree, or on the plattform for the Kållerado river rapids ride, which is not running - it would have made you really wet and cold!) Turning right just before the ponies, you pass the "Frog hopper", which is the small cousin of the large drop towers up on the mountain.
But now, continue through the park, enjoy the lights, and the little shops. Most amusement park investigations are better performed in the summer - and you do not need to know that the shape of the chains is called a catenary (and is actually a cosh(x)), nor that each of the chains of light from the tower is loaded by a 700kg weight to keep it in place, to enjoy the large Christmas tree.