$A$ particle of mass $m$ moves along line $PC$ with velocity $v$ as shown in the figure. What is the angular momentum of the particle about point $O$?

$A$ particle is moving in a circular path of radius $a$ with a constant speed $v$ as shown in the figure. The centre of the circle is marked by $C$. The angular momentum about the origin $O$ can be written as:

Derive the equation of angular momentum in the case of rotational motion about a fixed axis.

$A$ ball of mass $m$ moving with velocity $v$ collides with a wall elastically as shown in the figure. After the impact,the change in angular momentum about point $P$ is:

$A$ particle with position vector $\overrightarrow{r}$ has a linear momentum $\overrightarrow{p}$. Which one of the following statements is true in respect of its angular momentum $\overrightarrow{L}$ about the origin?

$A$ particle of mass $m$ is moving in time $t$ on a trajectory given by $\overrightarrow{r} = 10 \alpha t^2 \hat{i} + 5 \beta (t - 5) \hat{j}$. Where $\alpha$ and $\beta$ are dimensional constants. The angular momentum of the particle becomes the same as it was for $t = 0$ at time $t = \dots$ seconds.