What is the principle of conservation of energy?

The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another or transferred from one object to another. The total energy of an isolated system remains constant over time. This fundamental concept underpins many scientific disciplines and can be expressed mathematically as:

${}_{}={}_{}\backslash text\{Total\; Energy\}\_\{\backslash text\{initial\}\}\; =\; \backslash text\{Total\; Energy\}\_\{\backslash text\{final\}\}$​

In practical terms, it means that the energy in a system, such as kinetic energy, potential energy, thermal energy, or chemical energy, may change forms but the overall amount of energy remains unchanged. For example, in a pendulum, the energy alternates between kinetic energy and potential energy, but the sum of both energies remains constant if no external forces (like friction) are acting on it.