Final answer:
To find the new angular velocity of the merry-go-round, use the concept of conservation of angular momentum. Calculate the initial angular velocity using the given moment of inertia and radius. Then calculate the new moment of inertia and use it to find the new angular velocity.
Step-by-step explanation:
To find the new angular velocity of the merry-go-round, we can use the concept of conservation of angular momentum. Initially, the merry-go-round is at rest, so its angular momentum is zero. When the children walk inward and stop at a distance of 0.75 m from the axis of rotation, the total angular momentum of the system must still be zero. The moment of inertia of the merry-go-round is given as 1000.0 kg. m². Since the radius of the merry-go-round is 4.0 m and the moment of inertia is 1000.0 kg. m², we can calculate the initial angular velocity using the formula:
Angular velocity = (moment of inertia) / (radius²)
After the children move inward, the total moment of inertia will change due to their new location. We can calculate the new angular velocity using the same formula but with the new moment of inertia. The moment of inertia will decrease because the children are closer to the axis of rotation. Therefore, the new angular velocity will be higher than the initial angular velocity.