Joule-second

The joule-second (J s, or J⋅s) is the product of an SI derived unit, the joule (J), and an SI base unit, the second (s).[1] The joule-second is a unit of action or of angular momentum. The joule-second also appears 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⋅m2 and its angular velocity in units of rad⋅s−1. This product of moment of inertia and angular 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).

Not to be confused with Joule/second.

Base units

In SI base units the joule-second becomes kilogram-meter 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).

Joules per second: 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 unit watt (W), which is joule per second (J/s).

joules-second: To understand joules x second (J⋅s) we can imagine the operator of an energy storage facility quoting a price for storing energy. Storing 10,000 joules for 400 seconds would cost a certain amount. Storing double the energy for half the time would use the same resources, and cost the same. Another example is the use of kilowatt-hour as a unit of energy. In this case, we are using the rate of energy output multiply by the time over which the output exists, to represent the total energy[3]. In other words, to understand what Joules * seconds means, one must understand the terms by themselves. The Joule is a unit of energy and the second is a unit of time. So, what 500 J.s means, is that there is a source of energy that I can use in the following manner: 500 Jules for 1 second; or 250 Jules for 2 seconds; or 100 Jules for 5 seconds; or 1 Jule for 500 seconds; or in any combination of numbers who's product is 500![4]

See also

References
  1. 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.
  2. 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.
  3. "User DJohnM". Physics Stack Exchange. Retrieved 2020-07-18.
  4. "User Guill". Physics Stack Exchange. Retrieved 2020-07-18.
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