Final answer:
The Ferris wheel experiences gravitational, normal, and frictional forces that affect the system's angular velocity and momentum, changing with the weight distribution as people move around it.
Step-by-step explanation:
When a Ferris wheel with people seated at positions 4 o'clock, 1 o'clock, 9 o'clock, and 6 o'clock begins to rotate, several forces come into play. These include the gravitational force, the normal force exerted by the structure of the wheel, and the frictional force at the axle. The gravitational force acts downwards, which causes the wheel to experience torque that will affect both its angular velocity and angular momentum. As people ascend or descend on the wheel, the distribution of weight changes, which in turn changes the moment of inertia and possibly affects the angular velocity of the wheel due to the conservation of angular momentum.
The normal force keeps the system in equilibrium and works against gravity. The frictional force is essential for allowing the wheel to turn smoothly around its axis and is also responsible for slowing down the rotation due to resistive forces.
The sum of these forces and the way they are applied will determine the steady state of angular velocity and will be reflected in changes to the angular momentum of the system, based on external factors like air resistance and the starting torque provided by the motor or other propulsion method.