The time dependence of the position of a particle of mass $m = 2$ is given by $\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j$ Its angular momentum with respect to the origin at time $t = 2$ is

The direction of the angular velocity vector along

A spherical shell of $1 \,kg$ mass and radius $R$ is rolling with angular speed $\omega$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin $O$ is $\frac{a}{3} R^{2} \omega$. The value of a will be ..............

Two rigid bodies $A$ and $B$ rotate with rotational kinetic energies $E_A$ and $E_B$ respectively.  The moments of inertia of $A$ and $B$ about the axis of rotation are $I_A$ and $I_B$ respectively. If $I_A = I_B/4 \,$and$ \, E_A = 100\ E_B$ the ratio of angular momentum $(L_A)$ of $A$ to the angular momentum $(L_B)$ of $B$ is

Given $V _{ CM }=2\; m / s , m =2\; kg , R =4\; m $

Find angular momentum of ring about origin if it is in pure rolling. $kgm ^{2} / s$

A disc of mass  $M$  and radius  $R$  is rolling with angular speed $\omega $ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin $O$ is