Conservation Laws

Conservation law, also known as law of conservation, in physics, a principle that states that a certain physical property (i.e., measurable quantity) within an isolated physical system it does not change in the course of time. 

In any physical phenomena, few physical quantities associated with the phenomena may change with time and few physical quantities associated with it may not change. Those physical quantities which remain constant in time are known as conserved quantities.

For example, if a big liquid drop is sprayed into several small droplets the volume of liquid before spraying and after spraying remains same. Hence, we can say that a physical quantity called volume is conserved in this example. Similarly, we have several quantities which are conserved. Within the scope of our course, we can discuss the following conservation laws.

1. Law of conservation of linear momentum

2. Law of conservation of energy

3. Law of conservation of angular momentum

Let us discuss them in brief.

Law of conservation of linear momentum

The linear momentum of a body is defined as the ability of a body by virtue of which it imparts its motion to other objects along a straight line. And mathematically it is equal to the product of mass of the body (m) and its velocity () Mathematically, .

According to this law, in absence of an external force, the total vector sum of linear momentum remains unchanged.

Example: When a bullet is fired with a gun, the total momentum vector of the system of bullet and gun is zero. After firing, bullet moves in forward direction with some momentum and gun recoils with the same amount of momentum in magnitude, but opposite in direction. Hence total vector sum of momentum after firing is also zero. Thus linear momentum of the system before and after firing is zero. Hence we can say that linear momentum is conserved.

Law of conservation of energy

According to this law the total energy of an isolated system is always constant and it never changes. But it can be transformed from one form to another. For example an electric cell in our daily life gives electrical energy by transforming chemical energy in it, electric motor converts electrical energy to mechanical energy, etc. However the total energy in these processes is conserved.

When an object is dropped from a certain height the total mechanical energy of the body is conserved. At its highest point all its mechanical energy will be in the form of potential energy and at its lowest point it will be in the form of kinetic energy, i.e. energy has transformed from one form into another, (i.e. potential to kinetic) but the total energy remains constant. Hence the total mechanical energy is conserved.

But this conservation of mechanical energy can’t be applied in the presence of non – conservative force. For example in the above case if you consider air resistance on the freely falling body total mechanical energy does not remain constant. Here work done by air resistance gets converted into different forms of energy like heat energy. So while applying energy conservation principle heat energy should also be taken into consideration in such cases

Law of conservation of angular momentum

Angular momentum () of a body about a point is defined as the cross product of its position vector about that point () and its linear momentum at that instant ()

i.e.

or L = rp sin θ where θ is the angle between ‘’ and ‘’.

According to this law the total angular momentum of the system remains conserved in absence of external torque.

Example: We know that planets revolves around sun in elliptical orbits. The angular momentum of a planet at any point during its motion in its path is conserved. We will study more clearly about this under rotatory motion concepts.

These are the few conservation laws in mechanics. Now let us discuss a conservation law in electrostatics.

Law of conservation of charge

This law states that the total electric charge of an isolated system is always conserved. Charge can neither be created nor destroyed, but it can be transferred or exchanged from one body to another.

Apart from these, there are several other physical quantities that are conserved in nature. During our further discussions in various chapters we will understand them.