Angular Momentum of a Particle
L = r × p = mr²ω — rotating ball with L vector (out of page).
Key Notes
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).
Formulas
Angular momentum (vector)
Cross product — direction by right-hand rule.
Magnitude
r_perp = perpendicular distance from O to line of motion.
Torque-angular momentum
Analog of F = dp/dt.
Conservation
No external torque ⇒ L conserved.
Particle on circular orbit
I = mr² for a point mass.
Important Points
L depends on the REFERENCE POINT — there is no 'absolute' angular momentum.
L of a particle moving in a straight line is NOT zero — it's m·v·r_perp about an external point.
Central force (like gravity): no torque about the force center ⇒ L conserved ⇒ equal areas swept in equal times.
Angular momentum vector for orbital motion is perpendicular to orbital plane.
Conservation of L explains why pulsars spin faster after collapse (I shrinks, ω rises).
L is the rotational analog of linear momentum but has DIFFERENT direction structure (perpendicular to motion plane).
Angular Momentum of a Particle notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.