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For an isolated system, total energy remains constant. For a system exchanging energy with its surroundings, its energy change equals the net transfer into it.
By Matan · Updated
Choose the system
A slowing bicycle loses mechanical energy while brakes, tyres and surroundings gain internal energy. The result depends on which bodies are inside the boundary. A thermodynamically closed system does not exchange matter but can exchange energy; isolated means neither matter nor energy crosses the boundary. [1]
Worked brake-energy balance
An idealised 80 kg bicycle-and-rider system slows from 5.0 m/s to rest on level ground. Translational kinetic energy decreases by ½ × 80 × 5² = 1000 J. If that is the only changing mechanical-energy term and all the energy goes into the included brakes and surroundings, their combined internal energy increases by 1000 J. Real rotating wheels add another kinetic-energy contribution.
Mechanical energy need not be conserved
Kinetic plus potential energy remains constant in the familiar conservative model. Friction, deformation or external work can change that sum. The total balance must still include the associated energy transfers. [1]
Conservation and usefulness differ
Conservation alone does not explain every efficiency limit; direction of thermal processes also matters. Continuous useful output needs an energy source. Ideal motion that continues without losses is different from a device delivering unlimited work without input.
Scope of this explanation
This article concerns ordinary mechanical-system accounting. A single conserved global “energy of the whole expanding universe” requires additional care in general relativity and is not established by this introductory balance.
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How this article was checked
Sources checked; calculations checked where shown. The definitions, model assumptions and main explanatory claims were cross-checked against the sources below. Worked-example arithmetic and units were checked separately. These examples are illustrative calculations, not experimental measurements.
Source cross-check and editing assisted by AI. No independent human scientific review is recorded for this revision. The check applies to the version dated 10 September 2026; it is not a guarantee that every possible interpretation is correct.
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Sources and further reading
- OpenStax: System energy conservation — System energy conservation.
Cite this article
Matan. “The Law of Conservation of Energy.” Your Physicist. Originally published 2026-06-11; updated 2026-09-10. https://your-physicist.com/the-law-of-conservation-of-energy/
Revision history
: Corrected closed versus isolated system terminology and separated total from mechanical energy with a checked braking example. Added linked sources and a transparent verification record.
