$A$ time varying force $F = 2t$ is applied on a spool rolling as shown in figure. The angular momentum of the spool at time $t$ about bottommost point is:

$A$ uniform rod is fixed to a rotating turntable so that its lower end is on the axis of the turntable and it makes an angle of $20^o$ to the vertical. (The rod is thus rotating with uniform angular velocity about a vertical axis passing through one end.) If the turntable is rotating clockwise as seen from above. What is the direction of the rod's angular momentum vector (calculated about its lower end)?

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 angular momentum of a particle performing uniform circular motion is $L$. If the kinetic energy of partical is doubled and frequency is halved, then angular momentum becomes

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 ..............

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