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

$A$ 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

When a particle is moving in a circular path around a fixed point in a plane,the direction of its angular momentum is ........

$A$ 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 $\omega \text{ rad/s}$ about the vertical axis. About the point of suspension:

$A$ 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).

If the Earth is considered a sphere of radius $R$ and mass $M$,then its angular momentum about its axis of rotation in terms of the time period $T$ will be: