# Joule-second

The **joule-second** (J s, or J∙s) is the mathematical product of an SI Derived Unit, the joule (J), and an SI Base Unit, the second (s).[1] The joule-second describes the amount of action occurring in a physical system through a summation of energy (or heat, or work) over time. In mathematical terms, this summation of energy means that the quantity of energy becomes integrated over time.

## Base units

In SI base units the joule-second becomes kilogram-meters squared-per second or kg∙m^{2}∙ s^{−1}. Dimensional Analysis of the joule-second yields M L^{2} T^{−1}. Note the denominator of seconds (s) in the base units.

## Confusion with joules per second

The joule-second *should not be confused* with the physical process of joules **per** second (J/s). In physical processes, when the unit of time appears in the denominator of a ratio, the described process occurs at a rate. For example, in discussions about speed, an object like a car travels a known distance of kilometers spread over a known number of seconds, and the car’s rate of speed becomes kilometers **per** second (km/s). In physics, work **per** time describes a system’s power; defined by the units of Watts (J/s), or joules per second.

## Other uses

The joule-second also appears as the unit of measure in classical mechanics for the angular momentum of a rotating object, and in quantum mechanics within the definition of Planck's constant.[2] Angular momentum is the product of an object’s moment of inertia, in units of kg∙m^{2} and its rotational velocity in units of m∙s^{−1}∙m^{−1}, or simply s^{−1} (i.e., Hz). This product of moment of inertia and rotational velocity yields kg∙m^{2}∙ s^{−1} or the joule-second. Planck's constant represents the energy of a wave, in units of joule, divided by the frequency of that wave, in units of s^{−1}. This quotient of energy and frequency also yields the joule-second (J∙s).

## References

- BIPM.
*Le Système international d’unités / The International System of Units (‘The SI Brochure’)*. Bureau international des poids et mesures, eighth edition, 2006, updated 2014. URL http://www.bipm.org/en/si/si_brochure/, ISBN 92-822-2213-6. - Schlamminger, S.; Haddad, D.; Seifert, F.; Chao, L. S.; Newell, D. B.; Liu, R.; Steiner, R. L.; Pratt, J. R. (2014). "Determination of the Planck constant using a watt balance with a superconducting magnet system at the National Institute of Standards and Technology." Metrologia. 51 (2): S15. arXiv:1401.8160 . Bibcode:2014Metro..51S..15S. doi:10.1088/0026-1394/51/2/S15. ISSN 0026-1394.