1.1: Guidelines for studying dynamics

This textbook aims to bring you basic understanding of dynamics and provide an engineering toolbox by which you can solve many problems in dynamics, both analytically and numerically. However, it is important to learn how to use this toolbox to apply it in new situations. The only way to learn this well is to solve problems. For this reason, it is very important, after having studied a part of the textbook, to practice solving problems yourself. Always first try to solve the problem yourself before looking at the solution, since you learn much more by finding the solution yourself, even if that costs more time. Getting stuck in solving a problem is probably the experience from which you learn the most. It points out what parts you don’t understand well enough, encourages you to study those parts better by reading the book or looking at similar examples, and after solving the problem the experience will ensure you will not easily forget how to solve similar problems. So, don’t give up too early or look at the solution, if you persist you often will manage.

Besides teaching you the basics of dynamics, an important aim of this textbook is to teach you to get rid of ’bad habits’ you might have acquired in high school by implementing the following guidelines:

1. Work with equations instead of filling in numerical values while analysing a problem. The aim is to learn how to solve problems with equations instead of filling in numbers at an early stage. Not only are you more likely to make errors when filling in numbers, it is also much harder to detect those errors afterwards (e.g. by checking units). Moreover, when having an equation as solution, it has a larger degree of validity and can be used to predict trends and optimise designs. Only fill in numbers after having reached the final equation.
2. Work with vectors instead of scalars. A position, force, moment, velocity or acceleration in 2 or 3 dimensional space is always a vector. Therefore you should initially always use vector notation in \(2 D\) and 3D, and only work with scalar values when appropriate, e.g. after having projected the vectors on a coordinate axis. Correct vector usage and notation will become increasingly important when you progress with your studies, so best get used to it early. Note that most problems in this book will focus on motion in the 2-dimensional \(x y\)-plane. Nevertheless, even in that case moment and angular velocity vectors point along the \(z\) direction. Moreover, most vector equations that are presented in this textbook will still be valid in \(3 \mathrm{D}\), unless they have a subscript \(2 D\).
3. Using a structured approach instead of jumping to conclusions too soon. In the analysis of dynamic systems, we will not assume anything, but use structured procedures to solve problems. For example, if a mass moves over a surface, we will not jump to the conclusion that the upward normal force equals the weight of the mass (which is not always the case for a curved surface), but determine the normal force from Newton’s laws.
4. Solve problems based on understanding, instead of by memorising example problems, and copying the methodology without understanding how it works. Although this memorising and solving many standard problems might seem effective for passing exams, it will leave you helpless when you encounter a problem that you did not see before. Therefore, focus on building understanding and ask questions if things are not clear.

This textbook aims to form a bridge between high-school physics and academic literature, providing more rigorousness and insight into the material. Available textbooks are often either too advanced and complex, or do not offer sufficient depth, insight or rigorousness in my view. This textbook provides a solid basis in dynamics of which I hope that it will help you to bridge the gap towards understanding more advanced academic books and articles.