A conservation law in the physical world is a consequence of some symmetry. A number of conservation laws exist. Some of them are exact and some are approximate. There are conservation laws pertaining to energy, momentum, angular momentum, charge, number of baryons (protons, neutrons and heavier elements), strangeness and various quantities. In this book, we are mainly interested in the conservation of energy, momentum and angular momentum. The conservation laws are powerful tools because of the following:

1. Conservation laws are independent of the details of trajectory and often of the details of the particular force.

2. Conservation laws may be used even when the force is not known. This applies particularly in the physics of elementary particles.

3. Conservation laws have an intimate connection with invariance.

4. Even when the force is known exactly, a conservation law may be a convenient help in solving for the motion of a particle.

Elastic and inelastic collisions

Generally, we consider collision between two bodies. A collision between two bodies may be either elastic or inelastic. In an elastic collision, total kinetic energy of the two bodies before collision is equal to the total kinetic energy of the bodies after collision. That is, in an elastic collision, the kinetic energy of the system of bodies is conserved. However, the kinetic energy may be shared among the bodies during collision. On the other hand, in an inelastic collision, the kinetic energy of the system is not conserved.

So far, in our discussion, we have assumed the existence of an inertial reference frame and all the experiments and theories have been developed for inertial reference frames. Reality seems to be otherwise. In fact, there is no inertial reference frame. Our laboratories are situated on the earth and any reference frame attached to the earth is not inertial reference frame, owing to its revolution around the sun and rotation about its own axis. The earth has translational motion which is not uniform and rotational motion. It is therefore doubly non-inertial. However, we cannot discard everything developed so far. We have already discussed with suitable reasoning that for practical purposes, the earth may be taken as inertial reference frame. Nevertheless, it is worth to discuss about the motions in non-inertial reference frames. An inertial reference frame moves with constant linear velocity. Thus, the deviation from non-inertial can be in two ways: (i) reference frame is moving with accelerated linear velocity and (ii) reference frame is moving with angular velocity. We shall handle the anomaly in two steps. First, we shall see how to make corrections when our reference frame is moving with linear acceleration with respect to an inertial reference frame. Next, we shall account for corrections when our reference frame is rotating with respect to an inertial reference frame.

Mechanics is a branch of science and technology where we deal with various kinds of motions of bodies. Based on the observations for the motions of bodies, Newton put forth three laws, often called the Newton's laws of motion. In the present chapter, we shall discuss about them. While discussing the Newton's laws of motion, we shall assume that the atmosphere around us is not imposing any force on the moving bodies. That is, we shall assume that the atmosphere is not present. For expressing the motion, we require some reference frame and a coordinate system.

Inertial reference frame

For describing motion of a body, we require a reference frame. Newton considered an absolute reference frame and a universal time. For an absolute reference frame, its origin as well as its axes are absolutely fixed. Distances (displacements) of bodies are measured with reference to this reference frame.

The reference frame in which Newton's laws of motion are valid is known as an inertial reference frame. In fact such a reference frame does not exist, as no material body is at absolute rest and therefore we cannot have an absolute reference frame. Even a reference frame attached to the earth is not an absolute one, as the earth revolves around the sun, as well as it spins about its own axis. Further, sun also moves in our galaxy, the Milky Way. In fact, no body in the universe is at the absolute rest.

Fundamentals of Mechanics is the culmination of our years of experience in research and teaching the subject. It takes into account our close observations of student responses. Furthermore, it is a sincere attempt to make the study of mechanics enjoyable and arouse interest in the subject. Mechanics, as a subject of physics, is taught at BSc and BTech level. Professor Suresh Chandra conceptualized the book to fulfill requirements of science and engineering students of this level. The other two authors put in their extensive effort to give it a shape of a comprehensive textbook. There are chapters on vectors, laws of motion, conservation laws, inverse-square-law forces, harmonic oscillator, theory of relativity and non-inertial reference frames to match the title with the syllabuses of mechanics at different universities. The chapters are supplemented by ample number of exercises and diagrams which would help in better understanding of the subject. Multiple-choice questions and problems are provided at the end of each chapter to test progress after a lesson is taught.

It was only with the help, support and encouragement of a number of people that this project could come to fruition. First of all, we would like to express sincere thanks to our colleagues for their constructive criticism. Suresh Chandra is thankful to the authorities of the Lovely Professional University for their constant support. We also thank our family members for their kind cooperation and express our gratitude to Cambridge University Press India Pvt. Ltd. for publishing this book. Any suggestion for improvement of the book will be greatly appreciated and may be addressed through the publishers.