$A$ 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)?

A particle of mass $2\, kg$ is on a smooth horizontal table and moves in a circular path of radius $0.6\, m$. The height of the table from the ground is $0.8\, m$. If the angular speed of the particle is $12\, rad\, s^{-1}$, the magnitude of its angular momentum about a point on the ground right under the centre of the circle is …….. $kg\, m^2\,s^{-1}$

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 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 pendulum consists of a bob of mass $m=0.1 kg$ and a massless inextensible string of length $L=1.0 m$. It is suspended from a fixed point at height $H=0.9 m$ above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse $P=0.2 kg – m / s$ is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is $J kg – m ^2 / s$. The kinetic energy of the pendulum just after the lift-off is $K$ Joules.

($1$) The value of $J$ is. . . . . .

($2$) The value of $K$ is. . . . .

Give the answers of the questions ($1$) and ($2$)