Why is angular momentum perpendicular?
In simple terms angular momentum is just the rotation of any object.
The formula of angular momentum is:-
This formula possess cross product of "r" with "v" i.e. "r x v" (x denotes cross product)
This particular relation denotes that angular momentum is perpendicular to the radial vector.
Please see the discussion below.
In addition to what Reyan Roberth said:
Angular momentum is a vector, so it must have a direction assigned to it. (Even though it might not seem as logical as the direction of a vector in linear motion). The object could be a point mass being twirled on a string or a disk on an axle. It would not be logical for the direction of angular momentum to be the direction of instantaneous velocity of any molecule of the object at any moment of its rotation. (Remember that it could be a disk with all molecules going in a circle.) So that disallows using any direction in the plane of rotation for the direction of the momentum vector.
The only option remaining for consideration then, for the direction of the momentum vector, is a direction perpendicular to the plane of rotation.
Whether the direction should be up or down (for a clockwise horizontal rotation) was determined to be the convention using the right hand rule. So, for a clockwise horizontal rotation, the vector points down.
I hope this helps,