In an orbital motion,the angular momentum vector is

$A$ particle of mass $5 \ kg$ moves along the straight line $y = 2x + 4$ with a velocity of $3\sqrt{5} \ m/s$. Find its angular momentum about the origin in $kg \ m^2 \ s^{-1}$.

$A$ small particle of mass $m$ is projected at an angle $\theta$ with the $x$-axis with an initial velocity $v_0$ in the $x-y$ plane as shown in the figure. At a time $t < \frac{v_0 \sin \theta}{g}$,the angular momentum of the particle is

Two particles $A$ and $B$ are moving as shown in the figure. Their total angular momentum about the point $O$ is

Two cars $A$ and $B$ each of mass $10^3 \text{ kg}$ are moving on parallel tracks separated by a distance of $10 \text{ m}$, in the same direction with speeds $72 \text{ km/h}$ and $36 \text{ km/h}$. The magnitude of angular momentum of car $A$ with respect to car $B$ is . . . . . . $\text{J} \cdot \text{s}$.

$A$ particle of mass $= 5 \text{ units}$ is moving with a uniform speed $V = 3 \sqrt{2} \text{ units}$ in the $XOY$ plane along the line $Y = X + 4$. The magnitude of the angular momentum of the particle about the origin is ...... $\text{units}$.