Final answer:
The angular momentum vector of an object rotating clockwise in a horizontal circle points downwards along the axis of rotation, determined by using the right-hand rule.
Step-by-step explanation:
The direction of an object's angular momentum vector when it is moving in a horizontal circle in a clockwise direction is determined using the right-hand rule. This rule states that if you curl the fingers of your right hand in the direction of rotation (clockwise in this case), your thumb will point in the direction of the angular momentum vector.
Since the object is rotating clockwise, as viewed from above, the angular momentum vector will point downwards along the axis of rotation, perpendicular to the plane of rotation.
Using the right-hand rule, the angular momentum vector points in the direction shown in part (b). The sum of the angular momenta of all the mass segments contains components both along and perpendicular to the axis of rotation.
Thus, the component along the axis of rotation is the only component that gives a nonzero value when summed over all the mass segments.