6.6: Choose and draw coordinate systems
After and while sketching the objects and forces, one or more relevant coordinate systems should be chosen. The choice of the coordinate system (CS) and its orientation is important, since a smart choice can significantly simplify the analysis. In most cases Cartesian coordinates are preferred. If you know the direction of a force (like the gravitational force or the contact force with the ground), it is often smart to align one of the coordinate axes with that force. Cylindrical coordinates are useful when objects rotate about a fixed rotation axis and \(t, n, b\) coordinates can be useful when point masses move along a constrained path, e.g. via a constraining rail object. In some cases a combination of coordinate systems can be used. In Figure 6.3 one can use Cartesian coordinates and align the \(y\)-axis with the gravitational acceleration vector, however one can also choose to use natural \(t, n, b\) coordinates with path coordinate \(s\). For demonstration, both are shown in the figure. It will become clear that in this situation \(t, n, b\) coordinates are easier to use \({ }^{2}\). After having chosen the CS it is drawn in the sketch with unit vectors according the guidelines from Sec. 3.3.