A body of mass $5 \mathrm{~kg}$ moving with a uniform speed $3 \sqrt{2} \mathrm{~ms}^{-1}$ in $\mathrm{X}-\mathrm{Y}$ plane along the line $\mathrm{y}=\mathrm{x}+4$.The angular momentum of the particle about the origin will be______________ $\mathrm{kg}\  \mathrm{m} \mathrm{s}^{-1}$.

A thin uniform rod, pivoted at $O$, is rotating in the horizontal plane with constant angular speed $\omega$, as shown in the figure. At time, $t =0$, a small insect starts from $O$ and moves with constant speed $v$ with respect to the rod towards the other end. It reaches the end of the rod at $t = T$ and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $(|\vec{\tau}|)$ on the system about $O$, as a function of time is best represented by which plot?

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

A particle of mass $m$ moves in the $XY$ plane with a velocity $v$ along the straight line $AB.$ If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B,$ then

The position vector of $1\,kg$ object is $\overrightarrow{ r }=(3 \hat{ i }-\hat{ j })\,m$ and its velocity $\overrightarrow{ v }=(3 \hat{ j }+ k )\,ms ^{-1}$. The magnitude of its angular momentum is $\sqrt{ x } Nm$ where $x$ is

A particle of mass $m$ moves along line $PC$ with velocity $v$ as shown.  What is the angular momentum of the particle about $O$ ​