Conservation of angular momentum in the context of Rifling

A tropical cyclone is a rapidly rotating storm system with a low-pressure area, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain and squalls. Depending on its location and strength, a tropical cyclone is called a hurricane (/ˈhʌrɪkən, -keɪn/), typhoon (/taɪˈfuːn/), tropical storm, cyclonic storm, tropical depression, or simply cyclone. A hurricane is a strong tropical cyclone that occurs in the Atlantic Ocean or northeastern Pacific Ocean. A typhoon is the same thing which occurs in the northwestern Pacific Ocean. In the Indian Ocean and South Pacific, comparable storms are referred to as "tropical cyclones". In modern times, on average around 80 to 90 named tropical cyclones form each year around the world, over half of which develop hurricane-force winds of 65 kn (120 km/h; 75 mph) or more.

Tropical cyclones typically form over large bodies of relatively warm water. They derive their energy through the evaporation of water from the ocean surface, which ultimately condenses into clouds and rain when moist air rises and cools to saturation. This energy source differs from that of mid-latitude cyclonic storms, such as nor'easters and European windstorms, which are powered primarily by horizontal temperature contrasts. Tropical cyclones are typically between 100 and 2,000 km (62 and 1,243 mi) in diameter. The strong rotating winds of a tropical cyclone are a result of the conservation of angular momentum imparted by the Earth's rotation as air flows inwards toward the axis of rotation. As a result, cyclones rarely form within 5° of the equator. South Atlantic tropical cyclones are very rare due to consistently strong wind shear and a weak Intertropical Convergence Zone. In contrast, the African easterly jet and areas of atmospheric instability give rise to cyclones in the Atlantic Ocean and Caribbean Sea.

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. There are also many approximate conservation laws, which apply to such quantities as mass, parity, lepton number, baryon number, strangeness, hypercharge, etc. These quantities are conserved in certain classes of physics processes, but not in all.

A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity which flows in or out of the volume.

A flywheel is a mechanical device that uses the conservation of angular momentum to store rotational energy, a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, assuming the flywheel's moment of inertia is constant (i.e., a flywheel with fixed mass and second moment of area revolving about some fixed axis) then the stored (rotational) energy is directly associated with the square of its rotational speed.

Since a flywheel serves to store mechanical energy for later use, it is natural to consider it as a kinetic energy analogue of an electrical inductor. Once suitably abstracted, this shared principle of energy storage is described in the generalized concept of an accumulator. As with other types of accumulators, a flywheel inherently smooths sufficiently small deviations in the power output of a system, thereby effectively playing the role of a low-pass filter with respect to the mechanical velocity (angular, or otherwise) of the system. More precisely, a flywheel's stored energy will donate a surge in power output upon a drop in power input and will conversely absorb any excess power input (system-generated power) in the form of rotational energy.

In aerospace engineering, spin stabilization is a method of stabilizing a satellite or launch vehicle by means of spin, i.e. rotation along the longitudinal axis. The concept originates from conservation of angular momentum as applied to ballistics, where the spin is commonly obtained by means of rifling. For most satellite applications this approach has been superseded by three-axis stabilization.

A rifle is a long-barreled firearm designed for accurate shooting, distinguished by having a barrel cut with a helical or spiralling pattern of grooves (rifling). Most rifles are designed to be held with both hands and braced against the shoulder via a buttstock for stability. Rifles are used in warfare, law enforcement, hunting and target shooting sports.

The invention of rifling separated such firearms from the earlier smoothbore weapons (e.g., arquebuses, muskets, and other long guns), greatly elevating their accuracy and general effectiveness. The raised areas of a barrel's rifling are called lands; they make contact with and exert torque on the projectile as it moves down the bore, imparting a spin. When the projectile leaves the barrel, this spin persists and lends gyroscopic stability to the projectile due to conservation of angular momentum, increasing accuracy and hence effective range. The class of firearm was originally termed the rifled gun, with the verb to rifle referring to the early modern machining process of creating grooves with cutting tools.

In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Being an observable, its eigenfunctions represent the distinguishable physical states of a system's angular momentum, and the corresponding eigenvalues the observable experimental values. When applied to a mathematical representation of the state of a system, yields the same state multiplied by its angular momentum value if the state is an eigenstate (as per the eigenstates/eigenvalues equation). In both classical and quantum mechanical systems, angular momentum (together with linear momentum and energy) is one of the three fundamental properties of motion.

There are several angular momentum operators: total angular momentum (usually denoted J), orbital angular momentum (usually denoted L), and spin angular momentum (spin for short, usually denoted S). The term angular momentum operator can (confusingly) refer to either the total or the orbital angular momentum. Total angular momentum is always conserved, see Noether's theorem.

In quantum mechanics, angular momentum coupling is the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta. For instance, the orbit and spin of a single particle can interact through spin–orbit interaction, in which case the complete physical picture must include spin–orbit coupling. Or two charged particles, each with a well-defined angular momentum, may interact by Coulomb forces, in which case coupling of the two one-particle angular momenta to a total angular momentum is a useful step in the solution of the two-particle Schrödinger equation.In both cases the separate angular momenta are no longer constants of motion, but the sum of the two angular momenta usually still is. Angular momentum coupling in atoms is of importance in atomic spectroscopy. Angular momentum coupling of electron spins is of importance in quantum chemistry. Also in the nuclear shell model angular momentum coupling is ubiquitous.

In astronomy, spin–orbit coupling reflects the general law of conservation of angular momentum, which holds for celestial systems as well. In simple cases, the direction of the angular momentum vector is neglected, and the spin–orbit coupling is the ratio between the frequency with which a planet or other celestial body spins about its own axis to that with which it orbits another body. This is more commonly known as orbital resonance. Often, the underlying physical effects are tidal forces.