Conservation of Angular Momentum
L = Iω conserved — pull string shorter, ω grows as (r₀/r)².
Key Notes
Conservation of angular momentum: if net external TORQUE on a system is zero, total L is conserved.
L = Iω. If I changes, ω compensates so that Iω stays constant.
Examples: figure skater pulls in arms → I drops → ω rises. Diver tucks → spins faster.
Holds about any FIXED axis or about the COM.
In the absence of external torque, an isolated rotating body keeps spinning forever.
Earth's day length is slowly INCREASING (~2.3 ms per century) because tidal friction transfers angular momentum to the Moon's orbit.
Astronomical examples: pulsars (collapsed stars) spin extremely fast because of conservation as r shrinks during collapse.
Conservation of L is INDEPENDENT of conservation of energy or linear momentum.
Formulas
Conservation
When net external torque vanishes.
Two-state form
Before vs after a configuration change.
ω from I
Smaller I ⇒ larger ω.
KE change during arm-pull
KE INCREASES when I drops (work done by internal forces).
Important Points
L is conserved when NO EXTERNAL TORQUE — internal forces (e.g., muscles) can change I but not L.
When a skater pulls in arms, KE INCREASES (despite L constant) — work done by muscles in pulling against centrifugal force.
Earth's rotation slows over geological time due to tidal torque from the Moon — angular momentum transferred to lunar orbit (Moon moves slightly farther away each year).
Conservation of L explains why galaxies, accretion disks, and protoplanetary nebulae are flat and rotating.
Common mistake: thinking ω is conserved. ω·I is conserved — separately, neither is.
Conservation of L is a DEEP symmetry: it follows from rotational invariance (Noether's theorem).
Conservation of Angular Momentum 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.