Two bodies $A$ and $B$ are rotating freely with moments of inertia $I_A$ and $I_B$ respectively. Given $I_A > I_B$ and their angular momenta are equal. If $K_A$ and $K_B$ are their rotational kinetic energies,then:

If a body completes one revolution in $\pi \ s$,then the moment of inertia is related to the rotational kinetic energy $(K)$ by which of the following expressions?

$A$ 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?

$A$ circular disc of mass $20 \ kg$ and radius $1 \ m$ is rotating about an axis passing through its center and perpendicular to its plane with an angular velocity of $2 \ rad \ s^{-1}$. Then the rotational kinetic energy of the disc is (in $J$)

$A$ solid sphere of mass $M$ and radius $R$ is rotating about its diameter. $A$ solid cylinder of the same mass and radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ($K_{\text{sphere}}$ to $K_{\text{cylinder}}$) will be:

$A$ flywheel rotating about a fixed axis has a kinetic energy of $360 \ J$ when its angular speed is $30 \ rad/s$. The moment of inertia of the wheel about the axis of rotation is ...... $kg \ m^2$.