This sphere example was used by Newton himself to discuss the detection of rotation relative to absolute space. Checking the fictitious force needed to account for the tension in the string is one way for an observer to decide whether or not they are rotating – if the fictitious force is zero, they are not rotating. (Of course, in an extreme case like the gravitron amusement ride, you do not need much convincing that you are rotating, but standing on the Earth's surface, the matter is more subtle.) Below, the mathematical details behind this observation are presented.