$A$ particle is moving along a straight line with increasing speed. Its angular momentum about a fixed point on this line

$A$ ring of mass $10 \ kg$ and diameter $0.4 \ m$ is rotated about its axis. If it rotates at $2100 \ rpm$,its angular momentum will be ........... $kg \cdot m^2/s$.

$A$ particle of mass $m$ is moving along a straight line parallel to the $x$-axis with a constant velocity $v$ at a distance $b$ from the origin. Find the angular momentum about the origin in vector form.

$A$ torque of $50 \ Nm$ acts on a body for $8 \ s$,which is initially at rest. The change in its angular momentum is:

$A$ uniform rod of mass $m$ and length $l$ is moving with velocity $u$ in a direction perpendicular to its length. $A$ blow of impulse $J$ is applied in the direction of $u$,perpendicular to its length at a distance $l/4$ from its center at point $P$,such that the instantaneous velocity of point $P$ is $2u$. Then the velocity of its center of mass will be:

$A$ 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 .......