Angular Momentum of a Particle

Angular momentum L of a particle about a point O: L = r × p, where r is the position vector from O and p = mv.

Magnitude: L = m·v·r·sin θ = m·v·r_perp, where r_perp = perpendicular distance from O to line of motion.

Units: kg·m²/s = J·s.

Direction: perpendicular to plane containing r and p (right-hand rule).

Torque is the rate of change of angular momentum: τ = dL/dt. If τ_ext = 0, L is conserved.

For a particle in uniform circular motion: L = mvr (constant magnitude, direction along axis).

Conservation of L is a fundamental law — distinct from conservation of linear momentum.

Examples: planets around the Sun (L conserved → Kepler's 2nd law), ice skater pulling in arms (L = Iω constant ⇒ ω rises as I drops).