$A$ uniform rod $AB$ of mass $m$ and length $l$ is at rest on a smooth horizontal surface. An impulse $P$ is applied to the end $B$. The time taken by the rod to turn through a right angle is

$A$ particle of mass $1 \ kg$ is moving with a linear velocity of $2 \ ms^{-1}$ parallel to the positive $X$-axis. During this motion,its minimum distance from the origin is $12 \ cm$. The angular momentum of this particle about the origin is ....... $Js$.

$A$ uniform rod of mass $8m$ and length $6a$ is placed on a horizontal table. Two point masses $m$ and $2m$ are moving with speeds $2v$ and $v$ respectively,as shown in the figure. They strike the rod and stick to it after the collision. Find the angular velocity of the rod about an axis passing through its center of mass.

$A$ particle of mass $100\,g$ is projected at time $t = 0$ with a speed $20\,ms^{-1}$ at an angle $45^{\circ}$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t = 2\,s$ is found to be $\sqrt{K}\,kg\,m^2/s$. The value of $K$ is $............$ (Take $g = 10\,ms^{-2}$)

Angular momentum is

$A$ 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 ........... $kg \cdot m^2/s$.