Physical World Test - 7

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge.

Mechanical energy is the sum of the potential and kinetic energies in a system. The principle of the conservation of mechanical energy states that the total mechanical energy in a system (i.e., the sum of the potential and kinetic energies) remains constant as long as the only forces acting are conservative forces.

The law of conservation of energy is thought to be valid across all domains of nature, from the microscopic to the macroscopic. It is routinely applied in the analysis of atomic, nuclear and elementary particle processes. At the other end. all kinds of violent phenomena occur in the universe all the time. Yet the total energy of the universe (the most ideal isolated system possible!) is believed to remain unchanged.

E = mc^{​​​​​2}, equation in German-born physicist Albert Einstein’s theory of special relativity that expresses the fact that mass and energy are the same physical entity and can be changed into each other.

In the equation, the increased relativistic mass (m) of a body times the speed of light squared (c^{​​​​​​2}) is equal to the kinetic energy (E) of that body.

The rate of change of the total momentum of a system does not change, meaning this quantity is constant, and proving the principle of the conservation of linear momentum: When there is no net external force acting on a system of particles the total momentum of the system is conserved.

The total linear momentum and the total angular momentum (both vectors) of an isolated system are also conserved quantities. These laws can be derived from Newton’s laws of motion in mechanics. But their validity goes beyond mechanics. They are the basic conservation laws of nature in all domains, even in those where Newton’s laws may not be valid.

Besides their great simplicity and generality, the conservation laws of nature are very useful in practice too. It often happens that we cannot solve the full dynamics of a complex problem involving different particles and forces. The conservation laws can still provide useful results. For example, we may not know the complicated forces that act during a collision of two automobiles; yet momentum conservation law enables us to bypass the complications and predict or rule out possible outcomes of the collision. In nuclear and elementary particle phenomena also, the conservation laws are important tools of analysis.

Conservation laws have a deep connection with symmetries of nature. For example, an important observation is that the laws of nature do not change with time! If you perform an experiment in your laboratory today and repeat the same experiment (on the same objects under identical conditions) after a year, the results are bound to be the same. It turns out that this symmetry of nature with respect to translation (i.e. displacement) in time is equivalent to the law of conservation of energy.

According to Michelson,"The more important fundamental laws and facts of physical science have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote."

The statement above is true. The validity of this incisive remark can be validated from the example of a moment of inertia. It states that the moment of inertia of a body depends on its energy. But according to Einstein's mass-energy relation (E = mc^{​​​​​2}), energy depends on the speed of the body.