Large playgrounds may offer a selection of different types of carousels, as shown in the figure on the top of the page.

Try them out! For the two carousels to the right of the top figure, or the pirouettes to the right you can try to  pull yourself closer to the center and then move out again. What happens? This is an illustration of conservation of  angular momentum, for forces directed towards the center. It also illustrates energy conversions, since you need to do work to pull yourself closer.

In slow carousels you can experience a number of ways to detect  rotation can be detected. You can e.g.  throw a ball to someone on the other side. You can let a small object on a string swing back and forth, as a miniature version of the Foucault pendulum. (Watch a short video from a carousel in Lund  and read the article How do we know the earth spins around its axis?)

Some carousels have an opening in the circle at the bottom (as the one in the middle of the second row). What do you think will happen to a ball rolling around the circle when it  reaches the opening?  Send a ball rolling around the circle and observe what happens! Were your expectations confirmed? 
(You can also try this experiment at home, by cutting a (disposable) circular pie shape in two pieces and let a ball roll around it and reach the opening.)