A ball of mass $1 \,kg$ is projected with a velocity of $20 \sqrt{2}\,m / s$ from the origin of an $x y$ co-ordinate axis system at an angle $45^{\circ}$ with $x$-axis (horizontal). The angular momentum [In $SI$ units] of the ball about the point of projection after $2 \,s$ of projection is [take $g=10 \,m / s ^2$ ] ( $y$-axis is taken as vertical)

Find the components along the $x, y, z$ axes of the angular momentum $l$ of a particle. whose position vector is $r$ with components $x, y, z$ and momentum is $p$ with components $p_{ r }, p_{ y }$ and $p_{z} .$ Show that if the particle moves only in the $x -y$ plane the angular momentum has only a $z-$component.

A $bob$ of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The $bob$ rotates in a horizontal circle with an angular speed $\omega\,  rad/s$ about the vertical. About the point of suspension

A uniform rod $A B$ of mass $2 \mathrm{~kg}$ and Length $30 \mathrm{~cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2\  \mathrm{Ns}$ is applied to end $B.$ The time taken by the rod to turn through at right angles will be $\frac{\pi}{\mathrm{x}}\  \mathrm{s}$, where  X=____

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

A bullet of mass $10\, g$ and speed $500\, m/s$ is fired into a door and gets embedded exactly at the centre of the door. The door is $1.0\, m$ wide and weighs $12\, kg$. It is hinged at one end and rotates about a vertical axis practically without friction . The angular speed of the door just after the bullet embeds into it will be