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The work–energy theorem says that net work on a constant-mass particle equals the change in its kinetic energy: Wnet = ΔK = ½mvf² − ½mvi².
By Matan · Updated
Sum the work of every force
For a constant force acting through a displacement, W = Fd cos θ. More generally, work is the path integral of force dotted with displacement. Sum all forces’ work before equating it to the particle’s kinetic-energy change. A force perpendicular to the displacement does no work on that motion. [1]
Worked example
A 2 kg object starts from rest. A push does +15 J of work and friction does −6 J. Net work is 9 J, so ½ × 2 × vf² = 9 and vf = 3 m/s. Counting the push alone would predict √15 m/s and miss the frictional energy transfer.
Work and potential energy
You can include gravity’s work directly in Wnet, or move it to the other side as a gravitational potential-energy change in a mechanical-energy balance. Do not count the same gravitational contribution twice. The work–energy theorem follows from Newton’s second law and does not require mechanical energy to remain constant. [1]
Choose the system carefully
For deforming or rotating extended bodies, account for internal and rotational energy where needed. Heat transfer is not automatically work on a particle. Total energy conservation concerns a complete energy balance, and an isolated system has no energy transfer across its boundary. The worked object above is an illustrative translational model.
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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: Work–energy theorem — Work–energy theorem.
Cite this article
Matan. “Work-Energy Theorem.” Your Physicist. Originally published 2023-03-17; updated 2026-09-10. https://your-physicist.com/work-energy-theorem/
Revision history
: Clarified net rather than applied work, added a friction example and separated particle kinetic energy from a complete energy balance. Added linked sources and a transparent verification record.
