anglemomentum

Anglemomentum is not a standard term in physics, but in informal usage it is often employed as a synonym for angular momentum, the quantity that describes rotational motion. In classical mechanics, angular momentum is defined by L = r × p, the cross product of position and linear momentum. For a single particle, the magnitude about an origin is L = m r v_perp, with v_perp the component of velocity perpendicular to r. For a rigid body rotating about a fixed axis, L = I ω, where I is the moment of inertia and ω is angular velocity. External torques τ change angular momentum according to dL/dt = τ; in the absence of external torque, angular momentum is conserved.

In quantum mechanics, angular momentum is represented by operators with discrete eigenvalues. Orbital angular momentum L^2 and L_z have eigenvalues ℓ(ℓ+1)ħ^2 and mℓħ, with ℓ = 0,1,2,... and mℓ ∈ {−ℓ, …, ℓ}. Spin is an intrinsic form of angular momentum, with S^2 and S_z eigenvalues s(s+1)ħ^2 and m_sħ, where s is the particle’s spin quantum number (for electrons, s = 1/2). The total angular momentum J = L + S has eigenvalues j(j+1)ħ^2 and m_jħ, with j in { |ℓ−s|, …, ℓ+s }.

Applications of angular momentum span many areas of physics. It explains stability of planetary orbits, the behavior of gyroscopes, and rotational dynamics of rigid bodies, as well as the fine structure of atomic spectra and selection rules in spectroscopy. In writing, anglemomentum is a nonstandard term; when precision is required, angular momentum, orbital angular momentum, spin, or total angular momentum should be used specifically depending on context.