joule second — from formula anatomyThe joule second (J·s) is the SI unit of action and angular momentum. Action is a fundamental quantity in physics that measures the 'amount of motion' over time, and it appears in the principle of least action that underlies all of classical mechanics. Angular momentum measures the rotational motion of a body and is conserved in isolated systems, making it one of the most important conserved quantities in physics, from spinning tops to planets orbiting stars.
The concept of action was introduced by Pierre Louis Maupertuis in the 1740s, and the principle of least action was refined by Euler and Lagrange. The unit as J·s became standard with SI. The Planck constant was introduced by Max Planck in 1900, giving the unit its quantum significance.
The unit is the product of energy (joules) and time (seconds). In classical mechanics, action is the integral of energy over time, and angular momentum is the product of moment of inertia and angular velocity, which also has units of J·s. In quantum mechanics, the Planck constant h has units of J·s, and it sets the scale for the quantization of action and angular momentum — for example, the angular momentum of an electron in an atom is an integer multiple of h/(2π).
It is used in quantum mechanics to describe the quantization of energy levels and angular momentum, and in engineering to specify the angular momentum of flywheels and gyroscopes.
The Planck constant is exactly 6.62607015 × 10⁻³⁴ J·s by definition since 2019, making the joule second the fundamental unit that defines the kilogram.
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