"The Volare". The chairs are suspended on ropes or cables and they swing around in circular motion. The angle that the cables make is determined by the balance of forces on the chair. Weight force down, tension force in the cables supplies the centripetal force on the chair. You must design a method to measure the angle that the cable makes to the vertical, a measurement of the radius of the chair and a method to measure the angular speed of the carousel.
I'm sure you will get the idea.
Enjoy the excursion.