The discussion centers on finding the angular velocity of a ball rolling inside a frictionless hemispherical bowl, expressed in terms of radius R, height y, and gravitational acceleration g. Initial calculations suggest that angular velocity is independent of height, but further analysis reveals that the angle q, which relates to the height, affects the vertical and horizontal components of the forces acting on the ball. The correct approach involves resolving the normal force and recognizing that centripetal force must balance the forces acting on the ball, leading to a dependency on height. The final expression for angular velocity can be derived using the relationship between velocity, radius, and gravitational forces. Understanding the geometry and forces involved is crucial for accurately determining angular velocity.