Rotating Axes

Abstract

So far in this text, we have made a great deal of fuss about choosing a fixed origin and axes before trying to solve mechanics problems. At first thought, this seems a straightforward requirement to satisfy. Further thought will, however, reveal the difficulty. The Earth is rotating about its axis, and the centre of the Earth rotates once a year around the Sun. Hence, in absolute terms, one is hard pressed to find a point that is not moving; there are, in reality, no absolutely fixed points. Well, do we discard the majority of the first ten chapters of this book? Of course not. In most applications, the fact that the origin is not truly stationary may be safely ignored on the grounds of scale. When we do the mathematics, we will make this clearer (see Section 11.4). It turns out that, only for a small class of problems, but a very important class of problems, it is mandatory to use axes that rotate. These are problems involving distances and times comparable to the radius of the Earth and the period of rotation of the Earth respectively. For a second class of problems, it is more convenient, and perhaps constructive, to use a rotating coordinate system. Problems that fall into this category include cars rounding corners and children throwing balls while on a roundabout. The use of a rotating coordinate system brings out well-known, but often poorly understood, concepts such as Coriolis ‘force’ and ‘centrifugal force’.