Kinetic Energy of Rotating+Translating Bar

[enkar]

If a cart is moving in the x-direction and has a bar (not a pedulum) attached to its center that will rotate, what are the terms of the kinetic energy? I'm having a hard time figuring out what the kinetic engery of the rotating+translating bar is. Can someone break it all down into each of the terms, please?

 

[arildno]

Since the bar is a rigid object(?), its kinetic energy may be written as:
KE=\frac{1}{2}m\vec{v}_{C.M}^{2}+\frac{1}{2}\vec{\omega}\cdot\vec{L}_{C.M}

Here, we have:
m-object's mass
\vec{v}_{C.M}-velocity of center of mass (C.M)
\vec{\omega}-rotational velocity of object
\vec{L}_{C.M}-angular momentum of object, computed relative yo C.M