A solid sphere of mass $500\,g$ and radius $5\,cm$ is rotated about one of its diameter with angular speed of $10\,rad \, s ^{-1}$. If the moment of inertia of the sphere about its tangent is $x \times 10^{-2}$ times its angular momentum about the diameter. Then the value of $x$ will be ..............

$A$ uniform disc is rolling on a horizontal surface. At a certain instant $B$ is the point of contact and $A$ is at height $2R$ from ground, where $R$ is radius of disc.

A metre stick is pivoted about its centre. A piece of wax of mass $20 \,g$ travelling horizontally and perpendicular to it at $5 \,m / s$ strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is $0.02 \,kg m ^2$, the initial angular velocity of the stick is ........... $rad / s$

Obtain $\tau = I\alpha $ from angular momentum of rigid body. 

A particle starts from the point $(0,8)$ metre and moves with uniform velocity of $\vec{v}=3 \hat{i} \,m / s$. What is the angular momentum of the particle after $5 \,s$ about origin is ........... $kg m ^2 / s$ (mass of particle is $1 \,kg$ )?

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______________ $\mathrm{kg}\  \mathrm{m} \mathrm{s}^{-1}$.