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.