Editing Energy

= Energy: Definition and Mathematical Representation =

== Introduction ==
'''Energy''' is a fundamental physical quantity that describes the capacity to perform work or produce change. It exists in many forms such as kinetic, potential, thermal, chemical, and nuclear energy. Energy is a conserved quantity—meaning it cannot be created or destroyed, only transformed from one form to another.

== Definition ==
In physics, energy is commonly defined through the work-energy principle:

<math>
W = \Delta E
</math>

Where:
* <math>W</math> is the work done,
* <math>\Delta E</math> is the change in energy of the system.

Energy can be kinetic, potential, thermal, or other types, depending on the system being considered.

== SI Unit ==
The SI unit of energy is the '''joule''' (J), defined as:

<math>
1\, \mathrm{J} = 1\, \mathrm{kg \cdot m^2 / s^2}
</math>

This is equivalent to the energy transferred when a force of one newton moves an object one meter.

== Forms of Energy ==

=== Kinetic Energy ===
Energy possessed by a moving object:

<math>
E_k = \frac{1}{2}mv^2
</math>

Where:
* <math>m</math> is the mass of the object,
* <math>v</math> is its velocity.

=== Potential Energy ===
Stored energy due to position or configuration. For gravitational potential energy near Earth's surface:

<math>
E_p = mgh
</math>

Where:
* <math>m</math> is the mass,
* <math>g</math> is acceleration due to gravity,
* <math>h</math> is height above a reference level.

=== Mechanical Energy ===
The sum of kinetic and potential energy in a system:

<math>
E_{\text{mechanical}} = E_k + E_p
</math>

=== Thermal Energy ===
Energy related to the temperature of a system due to the kinetic energy of its particles.

=== Chemical and Nuclear Energy ===
Stored in bonds between atoms and subatomic particles; released through chemical reactions or nuclear fission/fusion.

== Law of Conservation of Energy ==
The total energy in an isolated system remains constant:

<math>
E_{\text{initial}} = E_{\text{final}}
</math>

Or more generally:

<math>
\Delta E_{\text{total}} = 0
</math>

This is one of the most important principles in all of physics and engineering.

== Applications ==
Energy is central to:
* Mechanics
* Thermodynamics
* Electrodynamics
* Engineering and technology (power generation, transport, etc.)
* Environmental science and sustainability

== See Also ==
* [[Work (physics)]]
* [[Power]]
* [[Kinetic Energy]]
* [[Potential Energy]]
* [[Conservation Laws]]
* [[Thermodynamics]]