Rotational mass is usually called the moment of inertia. Note that angular velocity (using the symbol ?) is a vector. Convention puts the angular velocity vector along the axis of rotation.

Write out the angular velocity vector ω in terms of the two components described above. Take a time derivative of ω to get the angular acceleration α of the bar. When taking this derivative, you will ...

Before the car moves, the angular momentum of the Earth plus cars is: (magnitude only since the direction does not change) Since the cars have the same angular velocity as the Earth, I can add the ...