Orders of magnitude (angular momentum)

Angular momentum is a physical quantity that describes the rotational inertia and direction of an object or system. It is a vector quantity, meaning it has both magnitude and direction. The order of magnitude of angular momentum refers to the power of ten closest to its value when expressed in standard scientific notation (e.g., 10^-30 kg⋅m²/s, 10⁵ kg⋅m²/s). This provides a convenient way to compare the relative sizes of angular momenta found in different physical systems, spanning vastly different scales.

The units of angular momentum are typically kilogram meters squared per second (kg⋅m²/s) in the International System of Units (SI). Sometimes it is expressed as Joule-seconds (J⋅s), as angular momentum has the same physical dimensions as action.

The orders of magnitude of angular momentum vary enormously depending on the system under consideration. For example:

• Subatomic particles: Intrinsic angular momentum (spin) of elementary particles, like electrons, is quantized and on the order of ħ (h-bar), which is approximately 1.054 × 10^-34 J⋅s.

• Atoms and molecules: Atoms and molecules also possess angular momentum due to the motion of their electrons and nuclei. These values are typically also on the order of ħ or small multiples thereof. Molecular rotation and vibration can have larger angular momentum depending on the moment of inertia and rotational frequency.

• Everyday objects: A spinning top, a bicycle wheel, or a rotating fan can have angular momenta ranging from 10^-3 kg⋅m²/s to 10² kg⋅m²/s or higher, depending on their size, mass, and speed of rotation.

• Planetary bodies: Planets orbiting stars and rotating on their axes have extremely large angular momenta. For instance, the Earth's orbital angular momentum around the Sun is on the order of 10⁴⁰ kg⋅m²/s. The Earth's rotational angular momentum is approximately 7 x 10³³ kg⋅m²/s.

• Galaxies: Galaxies, which consist of billions of stars, gas, and dust, have even larger angular momenta, ranging from 10⁶⁷ kg⋅m²/s and upwards, contributing to their spiral structure.

Understanding the order of magnitude of angular momentum is crucial in various areas of physics, from quantum mechanics to astrophysics, allowing for quick estimations and comparisons of rotational phenomena across different scales.