$A$ molecule consists of two atoms each of mass $m$ and separated by a distance $d$. At room temperature,the average rotational kinetic energy is $E$. What is its angular frequency?

$A$ solid spherical ball of mass $1 \, kg$ and radius $3 \, cm$ is rotating with an angular velocity of $50 \, rad/s$ about an axis passing through its center. The rotational kinetic energy is:

$A$ solid cylinder of mass $M$ and radius $R$ is rotating about its geometrical axis. $A$ solid sphere of same mass and same radius is also rotating about its diameter with an angular speed half that of the cylinder. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder will be

Three particles are situated on a light and rigid rod along the $Y$-axis as shown in the figure. If the system is rotating with an angular velocity of $2 \, rad/s$ about the $X$-axis,then the total kinetic energy of the system is ...... $J$.

$A$ body is rotating about its own axis. Its rotational kinetic energy is $x$ and its angular momentum is $y$. Hence,its moment of inertia about its own axis is:

The moments of inertia of two freely rotating bodies $A$ and $B$ are $I_{A}$ and $I_{B}$ respectively. Given $I_{A} > I_{B}$ and their angular momenta are equal. If $K_{A}$ and $K_{B}$ are their kinetic energies,then: