$A$ thin rod $AB$ is sliding between two fixed right-angled surfaces. At some instant,its angular velocity is $\omega$. If $I_X$ represents the moment of inertia of the rod about an axis perpendicular to the plane and passing through the point $X$ ($A, B, C,$ or $D$),the kinetic energy of the rod is:

• A
  $\frac{1}{2} I_A \omega^2$
• B
  $\frac{1}{2} I_B \omega^2$
• C
  $\frac{1}{2} I_C \omega^2$
• D
  $\frac{1}{2} I_D \omega^2$