Rolling motion?

Question

A sphere rolls on a smooth plane with angular velocity omega. What is the angular momentum of the point of contact of the sphere with the surface

Answer 1

As an object rolls without slipping, the point in contact with the surface is instantaneously at rest.
If the point of contact with the ground is at rest it has no angular velocity, therefore it has no angular momentum.

Angular Momentum (L) equals Angular velocity (ω) * Rotational Inertia (I)
L = ω * I
If ω = 0, L = 0

Following this same logic, the point which is opposite the point of contact with the ground has an angular speed which is double the value corresponding to the overall sphere's angular velocity, giving it twice the angular momentum.
The two points which lie exactly in between the top and bottom of the sphere have an angular velocity equal to that over the overall sphere.