Final answer:
Your apparent weight on a Ferris wheel changes slightly at different points due to the speed of the wheel and centripetal force, but your actual weight due to gravitational force remains constant. The forces acting on a Ferris wheel with people at different positions include gravitational and centripetal forces, which affect the system's angular velocity and angular momentum.
Step-by-step explanation:
On a Ferris wheel, you do not significantly weigh more at either the top or bottom of the ride in the context of gravitational force, which is the primary force acting on you. However, your apparent weight can change based on the speed of the Ferris wheel and the centripetal force required to keep you in circular motion. At the bottom of the Ferris wheel, your apparent weight might be slightly more than your actual weight if the Ferris wheel is moving quickly because of the additional centripetal force required to change your direction of motion. Conversely, at the top, if the speed is significant, your apparent weight might be less, due to the centrifugal effect (an apparent force experienced in a rotating reference frame). When the ride is moving at a constant speed, the only force acting on you is gravitational force, therefore your weight wouldn’t differ much from your actual weight.
Considering a scenario of people seated at 4 o’clock, 1 o’clock, 9 o’clock, and 6 o'clock positions on a Ferris wheel, the primary forces acting on the system are gravitational force and centripetal force. As the wheel turns, the distribution of mass can affect the angular velocity and angular momentum, but in an ideal scenario with equal mass distribution and no friction, these should remain constant. Any changes in mass distribution, such as people leaning or moving, would have a minor impact on the system's dynamics.