Final answer:
The child closer to the axis of rotation moves with greater linear velocity.
Step-by-step explanation:
In this case, the child closer to the axis of rotation moves with greater linear velocity. The linear velocity of a point on a rotating object is given by the equation v = rω, where v is the linear velocity, r is the distance from the axis of rotation, and ω is the angular velocity. Since ω is the same for both children, the child closer to the axis of rotation will have a smaller distance (r), resulting in a greater linear velocity. Therefore, the correct answer is a) The one closer to the axis of rotation.