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The measure of rotational inertia of a body is equal to the moment of inertiaI of a body about a particular axis.

The expression for the rotational kinetic energy is given by,

$\mathit{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{I}{\mathit{蝇}}^{\mathbf{2}}$

Here, is the moment of inertia, and$\mathit{蝇}$ is the angular velocity of body.

Rotation about z-axis,

The kinetic energy of a diatomic molecule when it spins at the same angular speed about z-axis will be K. This is because the moment of inertial of the diatomic molecule about z-axis is equal to moment of inertial of the diatomic molecule about x-axis as angular speed is same.

Therefore, the required kinetic energy is K.

Rotation about y-axis,

The kinetic energy of diatomic molecule when it spins at the same angular speed about y-axis will be zero. This is because the moment of inertia of a diatomic molecule about y-axis is zero, since the molecules are as point masses.

Therefore, the required kinetic energy is 0.