$A$ particle is moving in a uniform circular motion with angular momentum $L$. If its angular frequency is doubled and its kinetic energy is halved,then the new angular momentum of the particle will be .......

$A$ ring and a solid sphere of the same mass and radius rotate with the same angular velocity about their respective diameters. Which of the following is true?

Two discs have moments of inertia $I_{1}$ and $I_{2}$ about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds $\omega_{1}$ and $\omega_{2}$ respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:

$A$ disc of circumference $s$ is at rest at a point $A$ on a horizontal surface when a constant horizontal force begins to act on its centre. Between $A$ and $B$ there is sufficient friction to prevent slipping,and the surface is smooth to the right of $B$. $AB = s$. The disc moves from $A$ to $B$ in time $T$. To the right of $B$,

$A$ thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $v$, the kinetic energy of the system is (neglect friction):

In the case of rotational dynamics,which one of the following statements is correct?
$[\vec{\omega} = \text{angular velocity}, \vec{v} = \text{linear velocity}, \vec{r} = \text{radius vector}, \vec{\alpha} = \text{angular acceleration}, \vec{a} = \text{linear acceleration}, \vec{L} = \text{angular momentum}, \vec{p} = \text{linear momentum}, \vec{\tau} = \text{torque}, \vec{f} = \text{force}]$