State and explain the law of conservation of angular momentum.

(N/A) The time rate of change of the total angular momentum $\vec{L}$ of a system of particles about a point (taken as the origin of the frame of reference) is equal to the sum of the external torques $\vec{\tau}_{ext}$ acting on the system.
$\therefore \frac{d \vec{L}}{d t} = \vec{\tau}_{ext}$
If the resultant external torque on the system is zero, i.e., $\vec{\tau}_{ext} = 0$, then:
$\frac{d \vec{L}}{d t} = 0$
This implies that $\vec{L} = \text{constant}$.
Law of conservation of angular momentum: "If the resultant external torque on a system is zero, then its total angular momentum remains constant."
Here, $\vec{L} = \text{constant}$ is equivalent to three scalar equations:
$L_{x} = K_{1}, L_{y} = K_{2}, \text{ and } L_{z} = K_{3}$
Where $K_{1}, K_{2}, \text{ and } K_{3}$ are constants, and $L_{x}, L_{y}, \text{ and } L_{z}$ are the components of the total angular momentum $\vec{L}$ along the $X, Y, \text{ and } Z$ axes respectively. The total angular momentum is conserved means that each of these components is conserved.