In any physical process involving the different forces, some physical quantities remain unchanged with time. Such quantities are called conserved quantities. The laws which govern the conservation of these quantities are called conservation laws.
In classical physics, we usually deal with the following four conservation laws:
1. Law of conservation of energy.
2. Law of conservation of linear momentum.
3. Law of conservation of angular momentum.
4. Law of conservation of charge.
What is an isolated system?
Any system (assembly of particles or bodies) on which no external force acts is called an isolated system.
LAW OF CONSERVATION OF ENERGY
This law states that energy can neither be created nor destroyed but it can be changed from one form to another. Equivalently, we can say that the total energy of an isolated system remains constant.
Examples:
(i) When a body falls freely, under gravity, its potential energy gradually changes into kinetic energy. But its total mechanical energy (kinetic energy + potential energy) remains constant at any point of its motion.
(ii) During the oscillation of a simple pendulum, the energy of the bob changes gradually from kinetic to potential as it moves from mean position to either extreme position. Tire energy changes from potential to kinetic as the bob moves from either extreme position to the mean position. At all points of its motion, total energy of the bob remains constant.
Some important point regarding conservation of energy:
> When a body moves under a conservative force, its total mechanical energy is conserved. In the presence of a non-conservative forces such as friction or air resistance, mechanical energy is not conserved. It changes into heat, sound, etc.
> Mechanical energy is conserved whether acceleration is constant or variable.
> In spite of all kinds of violent phenomena occurring in the universe all the time, the total energy of the universe remains constant. In fact, universe is an example of the most ideal isolated system possible. According to Albert Einstein, mass and energy are interconvertible. In 1905, he established the mass- energy equivalence. The energy associated with mass m is given by
E = mc2
where c is the speed of light in vacuum.
> As mass can be converted into energy, so in law of conservation of energy, we include mass also.
Law of conservation of linear momentum:
This law states if no external force acts on a system, then its linear momentum remains constant.
Examples:
(i) A rifle gives backward kick on firing a bullet. Before firing, both the bullet and the rifle are at rest and initial momentum of the system is zero. As soon as bullet is fired, it moves forward with a large velocity. In order to conserve momentum, the rifle moves backward with such a velocity that the final momentum of the system is zero.
(ii) Suppose a radioactive nucleus, initially at rest, decays spontaneously into fragments. To conserve momentum, the heavier and lighter fragments will fly in opposite directions, with the former having a proportionately smaller speed than the latter.
LAW OF CONSERVATION OF ANGULAR MOMENTUM
A body rotating about an axis has a rotational inertia, called moment of inertia. Also, it is associated with a momentum, called angular momentum. We shall prove later on that
Angular momentum (L) = Moment of inertia (I) × angular speed (ω)
The law of conservation of angular momentum states that if no external torque acts on a system, then its angular momentum remains constant.
Examples : (i) While revolving in its elliptical orbit, when a planet approaches the sun, its moment of inertia about the sun decreases. To conserve the angular momentum, its angular speed increases.
(ii) In a Tornado as the air rushes towards the centre, its moment of inertia decreases. To conserve the angular momentum, the angular speed of the air increases.
LAW OF CONSERVATION OF CHARGE
This law states that the total charge of an isolated system remains constant. This implies that the electric charges can neither be created nor destroyed, only they can be transferred from one body to another.
Examples : (/) When a glass rod is rubbed with silk cloth, both develop charges. It is observed that the positive charge developed on the glass rod has the same magnitude as the negative charge developed on silk cloth. So total charge after rubbing is zero as before rubbing i.e., electric charge is conserved.
(ii) Electric charge is conserved during the fission of a nucleus by a neutron.
Some important points:
> In classical physics, we deal with the four conservation laws of energy, momentum, angular momentum and charge. But in nuclear and particle physics, we also deal with the conservation of quantities like parity, baryon number, strangeness, hypercharge, etc.
> A conservation law is a hypothesis, based on observations and experiments. A conservation law cannot be proved. It can only be verified, or disproved, by experiments.
> Some conservation laws may hold for one fundamental force but not for the other. For example, parity is conserved by the strong and electromagnetic forces but not by the weak force. Also, strangeness is conserved by the strong force but not by the weak force.
RELATION BETWEEN CONSERVATION LAWS AND SYMMETRIES OF NATURE
Conservation laws are closely related to the symmetries of the nature. The symmetries of space, time and other types of symmetries have played an important role in developing the modern theories of fundamental forces.
(i) If we perform an experiment at a certain place today and repeat the same experiment after one year at the same place, we obtain exactly the same results. This symmetry of nature with respect to translation or displacement of time is called homogeneity of time and it leads to the law of conservation of energy. (ii) Laws of nature take the same form everywhere in the universe i.e., there is no preferred location in the universe. This symmetry of the laws of nature with respect to translation in space is called homogeneity of space and gives rise to the law of conservation of linear