To determine the direction of angular velocity, we use the right-hand rule. If the fan is rotating counterclockwise, the angular velocity vector points along the negative \( k \)-axis, indicating the direction of rotation.
A uniform circular disc of radius \( R \) and mass \( M \) is rotating about an axis perpendicular to its plane and passing through its center. A small circular part of radius \( R/2 \) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.