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). 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.
In SI base units the joule-second becomes kilogram-meters squared-per second or kg∙m2∙ s−1. Dimensional Analysis of the joule-second yields M L2 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.
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. Angular momentum is the product of an object’s moment of inertia, in units of kg∙m2 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∙m2∙ 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).
- 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.