$A$ mass $m$ is moving with a constant velocity $v$ along a line parallel to the $X$-axis. Its angular momentum with respect to the origin or the $Z$-axis is:

$A$ small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion in the $x-y$ plane with centre at $O$ and constant angular speed $\omega$. If the angular momentum of the system,calculated about $O$ and $P$ are denoted by $\vec{L}_O$ and $\vec{L}_P$ respectively,then

Explain the Cartesian components of the angular momentum of a particle.

$A$ ball of mass $1 \,kg$ is projected with a velocity of $20 \sqrt{2} \,m/s$ from the origin of an $xy$ coordinate axis system at an angle of $45^{\circ}$ with the $x$-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).

$A$ uniform rod of mass $M$ and length $L$ has an impulse $J$ applied at right angles to one end. If the other end begins to move with speed $V$,the magnitude of the impulse is:

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