3 Nature of Physical Laws

• Conserved Quantities

These are some special physical quantities that remain constant with time.

Example − Energy, linear momentum, angular momentum, charge, parity, etc.

• Law of Conservation of Energy

For motion under an external conservative force, the total mechanical energy (that is the sum of kinetic and potential energy of a body) remains constant.

Example − Free fall of an object under gravity

The sum of potential energy and kinetic energy of the ball remains the same at every point during its fall.

The law of conservation of energy is valid for any kind of transformation between different forms of energy or across all domains of nature from the microscopic to the macroscopic.

• Law of Conservation of Linear Momentum

In the absence of an external force, the linear momentum of a system remains unchanged.

• Law of Conservation of Angular Momentum

If the total external torque acting on a system is zero, then angular momentum of the system remains constant.

• Law of Conservation of Charge

Charges are neither created nor destroyed, but are simply transferred from one body to another.

In many cases, conservation laws simplify the problems.

Using conservation laws of energy and momentum for beta decay, Pauli predicted the existence of a new particle called neutrino emitted along with electron in β-decay.

Note

• Conservation laws have a deep connection with symmetries of nature. For example, laws of nature do not change with time.
• Laws of nature are the same everywhere in the universe.