Angular momentum, $|\mathbf{L}|$ or $L=I \omega$ (about axis of rod) Moment of inertia of the rod-insect system. $I=I_{\text {rod }}+m x^{2}=I_{\text {rod }}+m v^{2} t^{2}$ Here, $m=$ mass of insect $\therefore \quad L=\left(I_{\mathrm{rod}}+m v^{2} t^{2}\right) \omega$




Now $|\tau|=\frac{d L}{d t}=\left(2 m v^{2} t \omega\right)$ or $|\tau| \propto t$

i.e. the graph is straight line passing through origin.

After time $T, L=$ constant

$\therefore \quad|\tau| \text { or } \frac{d L}{d t}=0$

i.e., when the insect stops moving, $L$ does not change and therefore $T$ becomes constant.