Answer
The magnitude of the angular momentum of the particle is $increasing$.
Work Step by Step
We know the position $\overrightarrow{r}=4t^{2}\hat{i}-(2t+6t^{2})\hat{j}$.
Using derivative, we obtain $\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}=8t\hat{i}-(2+12t)\hat{j}$.
The angular momentum of the particle can be calculated using the equation:
$L=I\omega=mvr$
Since the mass is constant; the $magnitude$ of $\overrightarrow{r}$ is $positive$ and increases over time; the $magnitude$ of $\overrightarrow{v}$ is also $positive$ and increases over time.
So, we can conclude that the magnitude of the particle's angular momentum is $increasing$.
