The simpler forms of circular motion are uniform and uniformly accelerating circular motion, which are part of the primary and secondary school physics curriculum in most countries. The more complicated case, with constantly changing tangential acceleration, also appears in many course books at advanced levels.1 Indeed, this kind of movement is often present in everyday life. Take, for example, the typical school experiment of placing a glass of water on a tray suspended on strings, and then rotating the tray in a vertical circle. If one is skillful enough and rotates the tray at a high enough speed, not a single drop of water will flow out of the glass, even when it is upside down (see Fig. 1). A similar kind of motion investigated using a smartphone in Ref. 2.
Airplanes on air parades or roller coasters in amusement parks also often run along a curved...