Two wheels $A$ and $B$ are mounted on the same axis. The moment of inertia of wheel $A$ is $I_A$ and its angular velocity is $\omega_A$,while wheel $B$ is initially at rest. When they are coupled together by a clutch,they rotate with a common angular velocity $\omega$. What is the moment of inertia of wheel $B$?

• A
  $(I_A + I_B) \omega$
• B
  $\frac{I_A \omega_A - I_A \omega}{\omega}$
• C
  $\frac{I_A \omega_A + I_A \omega}{I_A}$
• D
  $\frac{I_A \omega_A + I_A \omega}{I_A \omega}$