Final answer:
The height of a Ferris wheel from the ground to the top is 30 feet, calculated by doubling the radius and adding the height of the cars off the ground. The angular velocity and angular momentum of the Ferris wheel are affected by forces such as gravity and the normal force; however, passenger distribution usually does not significantly affect these unless the distribution is imbalanced.
Step-by-step explanation:
The height of a Ferris wheel from the ground to the top of the wheel can be calculated by adding the height of the cars off the ground to the radius of the Ferris wheel. The radius is half the diameter. So, for a wheel with a diameter of 26 feet, the radius would be 13 feet. The cars are 4 feet off the ground, so the total height from the ground to the top of the wheel would be the radius (13 feet) times 2, plus the height of the cars off the ground, which gives us 26 feet + 4 feet = 30 feet.
Regarding the forces acting on a Ferris wheel with people in the chairs at the 4 o'clock, 1 o'clock, 9 o'clock, and 6 o'clock positions, gravity and the normal force are the primary forces at play. The distribution of the passengers at these positions will not significantly affect the angular velocity and angular momentum of the wheel unless their distribution is asymmetric and it is not balanced. If the mass distribution is imbalanced, it could cause the wheel to rotate unevenly. However, in a typical Ferris wheel ride, the design ensures even spacing of the cars and passengers for a smooth rotation.