$A$ solid cylinder of mass $20 \ kg$ rotates about its axis with an angular speed of $100 \ rad \cdot s^{-1}$. The radius of the cylinder is $0.25 \ m$. The magnitude of its angular momentum about the axis of the cylinder is ........ $J \cdot s$.

The position vector of a particle of mass $m$ moving with a constant velocity $\vec{v} = v \hat{i}$ is given by $\vec{r} = x(t) \hat{i} + b \hat{j}$, where $b$ is a constant. At an instant, $\vec{r}$ makes an angle $\theta$ with the $x$-axis. The variation of the magnitude of the angular momentum $|\vec{L}|$ of the particle about the origin with $\theta$ will be:

When the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ changes sign to $-\vec{r}$, which one of the following vectors will not flip its sign?

$A$ thin horizontal disc is rotating about a vertical axis passing through its fixed centre $O$. Its angular momentum is $L_A$ and $L_B$ computed about points $A$ and $B$, respectively, with $OB = 2 \times OA$. The value of $\frac{L_A}{L_B}$ is :

$A$ particle moves along a circular path with decreasing speed. Hence,

Which graph represents the relationship between angular momentum $L$ and angular velocity $\omega$ for a rigid body rotating about a fixed axis?