According to the principle of conservation of angular momentum, the rate of change of angular momentum of a system is equal to the net external torque acting on it, i.e., $\vec{\tau} = \frac{d\vec{L}}{dt}$. Therefore, if the net external torque acting on the system is zero ($\vec{\tau} = 0$), the rate of change of angular momentum is zero, which means the angular momentum of the system remains constant ($\vec{L} = \text{constant}$).