Angular momentum is conserved when no net external torque acts on a system, and the underlying laws are rotationally symmetric about the axis you’re considering.

Core rule (the short version)

  • If the net external torque on a system about some axis is zero, then its total angular momentum about that axis stays constant:
    τnet=dLdt=0⇒L=constant\tau_{\text{net}}=\dfrac{dL}{dt}=0\Rightarrow L=\text{constant}τnet​=dtdL​=0⇒L=constant.
  • This is the rotational analog of “no net force ⇒ linear momentum conserved.”

What “no net external torque” really means

  • Internal forces (forces particles inside the system exert on each other) do not change the total angular momentum of the system; they cancel in pairs if they act along the line joining the particles.
  • Only torques from outside the chosen system can change its angular momentum; if those torques add up to zero, angular momentum is conserved.
  • You must specify the axis (or point) about which you compute torque and angular momentum; conservation can hold about one point but not another if external torques differ.

Symmetry viewpoint (Noether-style)

  • Angular momentum conservation is deeply tied to rotational symmetry: if the laws of physics don’t change when you rotate space, then angular momentum is conserved (Noether’s theorem).
  • If some interaction picked out a preferred direction in space (breaking rotational symmetry), angular momentum about that direction would generally not be conserved.

Everyday and textbook examples

  • A figure skater pulling in their arms spins faster: moment of inertia III decreases, angular velocity ω\omega ω increases so that L=IωL=I\omega L=Iω remains constant (no significant external torque).
  • A planet orbiting the Sun in the two-body approximation keeps the same orbital angular momentum vector; gravity provides a central force, so the torque about the Sun is zero and the orbital plane stays fixed.
  • A spinning chair + dumbbells demo: pulling the dumbbells inward changes III but not LLL, so rotation rate increases; pushing them out slows the spin, again keeping LLL constant.

When angular momentum is not conserved

  • If a nonzero net external torque acts (for example, friction at a bearing, a person pushing on a door, or an off-center rocket thrust), then dL/dt=τnet≠0dL/dt=\tau_{\text{net}}\neq 0dL/dt=τnet​=0 and angular momentum changes with time.
  • In real-world systems, small external torques (air resistance, friction, non-central forces) gradually change angular momentum, so conservation is often an approximation rather than exact.

In one sentence: Angular momentum is conserved about an axis when the system experiences zero net external torque about that axis and the dynamics respect rotational symmetry.

Information gathered from public forums or data available on the internet and portrayed here.