Law of conservation of angular momentum:

If the total external torque acting on a particle is zero, then the angular momentum remains conserved. This is known as the law of conservation of angular momentum.

We know that the time rate of change of angular momentum of a particle is equal to the torque acting on it.

If \( \vec{L} \) be the angular momentum of a particle, then the torque acting on that particle is \( \vec{\tau}=\frac{d\vec{L}}{dt} \). [ To know the derivation, (CLICK HERE) ]

Now, if \( \tau=0 \), then \( \frac{d\vec{L}}{dt}=0 \), or, \( \vec{L}=Constant \).

So, when the total external torque acting on a particle is zero, then the angular momentum of the particle remains conserved.