# Solved Problems in Classical Mechanics

It is in the study of classical mechanics that we first encounter many of the basic ingredients that are essential to our understanding of the physical universe. The concepts include statements concerning space and time, velocity, acceleration, mass,momentum and force, and then an equation of motion and the indispensable law of action and reaction – all set (initially) in the background of an inertial frame of reference. Units for length, time and mass are introduced and the sanctity of the balance of units in any physical equation (dimensional analysis) is stressed. Reference is also made to the task of measuring these units – metrology, which has become such an astonishing science/art.

The rewards of this study are considerable. For example, one comes to appreciate Newton’s great achievement – that the dynamics of the classical universe can be understood via the solutions of differential equations – and this leads onto questions regarding determinism and the effects of even small uncertainties or disturbances. One learns further that even when Newton’s dynamics fails, many of the concepts remain indispensable and some of its conclusions retain their validity – such as the conservation laws for momentum, angular momentum and energy, and the connection between conservation and symmetry – and one discusses the domain of applicability of the theory. Along the way, a student encounters techniques – such as the use of vector calculus – that permeate much of physics from electromagnetism to
quantum mechanics.

All this is familiar to lecturers who teach physics at universities; hence the emphasis on undergraduate and graduate courses in classical mechanics, and the variety of excellent textbooks on the subject. It has, furthermore, been recognized that training
in this and related branches of physics is useful also to students whose careers will take them outside physics. It seems that here the problem-solving abilities that physics students develop stand them in good stead and make them desirable employees.

Our book is intended to assist students in acquiring such analytical and computational skills. It should be useful for self-study and also to lecturers and students in mechanics courses where the emphasis is on problem solving, and formal lectures are kept to a minimum. In our experience, students respond well to this approach. After all, the  rudiments of the subject can be presented quite succinctly (as we have endeavoured to do in Chapter 1) and, where necessary, details can be filled in using a suitable text.