Joule-second


The joule-second is the product of an SI derived unit, the joule, and an SI base unit, the second. 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.

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 in the base units.

Confusion with joules per second

The joule-second should not be confused with the physical process of joules per second.
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. In physics, work per time describes a system’s power; defined by the unit watt, which is joule per second.
joules-second: To understand joules x second 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. 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!