Two wheels are connected by a belt. The radius of the larger wheel is three times that of the smaller one. What is the ratio of the rotational inertia of the larger wheel to the smaller wheel,when both wheels have the same angular momentum?

$A$ 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?

$A$ mass '$M$' is moving with constant velocity parallel to the $X$-axis. Its angular momentum with respect to the origin is

$A$ uniform rod of mass $8m$ and length $6a$ is placed on a horizontal table. Two point masses $m$ and $2m$ are moving with speeds $2v$ and $v$ respectively,as shown in the figure. They strike the rod and stick to it after the collision. Find the angular velocity of the rod about an axis passing through its center of mass.

$A$ particle of mass $m$ is moving with constant velocity $v$ parallel to the $x$-axis as shown in the figure. Its angular momentum about origin $O$ is ..........

$A$ cylinder of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega$. $A$ particle of mass $m$ moving with velocity $v$ hits the cylinder and sticks to its rim. Calculate the angular velocity of the cylinder after the impact.