Does the moment of inertia affect angular momentum?
Note that the Law of Conservation of Angular Momentum states that total angular momentum is always conserved.
For example, suppose that an ice skater rotates at one spot about a fixed axis with arms outstretched, an with constant angular velocity
Suppose now that he moves his arms towards his centre and places them on his chest. Automatically his angular velocity will increase and he will begin to rotate faster in order to satisfy the principle of conservation of linear momentum. This is so since by pulling his arms inwards he decreases his moment of inertia since by definition
where r is the position vector from the axis of rotation to the mass element dm.