The joule-second (symbol J⋅s or J s) is the product of an SI derived unit, the joule (J), and an SI base unit, the second (s). 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. 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).
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.
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.