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 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 $bob$ 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 $\omega\,  rad/s$ about the vertical. About the point of suspension

A particle of mass $m$ is moving along the side of a square of side '$a$', with a uniform speed $v$ in the $x-y$ plane as shown in the figure

Which of the following statement is false for the angular momentum $\vec L$ about the origin ?

A particle moves with a constant velocity in $X-Y$ plane. Its possible angular momentum w.r.t. origin is

Obtain the relation between torque of a system of particles and angular moment.