$A$ particle starts from the point $(0, 8) \, m$ and moves with a uniform velocity of $\vec{v} = 3 \hat{i} \, m/s$. What is the angular momentum of the particle about the origin after $5 \, s$ (mass of the particle is $1 \, kg$)?

$A$ thin uniform rod of length $L$ and mass $m$ is kept on a frictionless horizontal table with a massless string of length $L$ fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point $O$. If a horizontal impulse $P$ is imparted to the rod at a distance $x = L/n$ from the mid-point of the rod (see figure), then the rod and string revolve together around the point $O$, with the rod remaining aligned with the string. In such a case, the value of $n$ is:

An object of mass $m$ is projected from the origin in a vertical $xy$ plane at an angle $45^{\circ}$ with the $x$-axis with an initial velocity $v_0$. The magnitude and direction of the angular momentum of the object with respect to the origin,when it reaches the maximum height,will be [$g$ is the acceleration due to gravity].

Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion.

Three equal masses $m$ are kept at vertices $(A, B, C)$ of an equilateral triangle of side $a$ in free space. At $t = 0$,they are given an initial velocity $\vec{V}_A = V_0 \hat{u}_{AC}, \vec{V}_B = V_0 \hat{u}_{BA}$ and $\vec{V}_C = V_0 \hat{u}_{CB}$. Here,$\hat{u}_{AC}, \hat{u}_{CB}$ and $\hat{u}_{BA}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally,then the magnitude of the net angular momentum of the system about the centroid of the triangle is:

The diameter of a flywheel is $1 \,m$. It has a mass of $20 \,kg$. It is rotating about its axis with a speed of $120$ rotations in one minute. Its angular momentum in $kg-m^2/s$ is (in $4$)