Angular Momentum of a Ferris Wheel

[quantum13]

Homework Statement

[Let a Ferris wheel exist.] The wheel carries 36 cars, each holding as many as 60 passengers of 70kg mass, around a circle of radius R = 38m. The mass of each car is about 1.1e4 kg. The mass of the wheel's structure as about 6.0e5kg, which was mostly in the circular grid from which the cars are suspended. Find the rotational inertia around the center of the wheel.

Homework Equations

I=MR²
L = Iω

The Attempt at a Solution

Divide the inertia into two parts, inertia of the cars and inertia of the wheel:
I_cars = MR²
M = [36 ( 1.1e4 + 60 x 70)] kg
R² = 38² m²

I_wheel = MR²
M = 6.0e5 kg
R² = 38² m²

Total inertia is calculated to be 1.7e9

Answer: 1.22e9
According to the solution, M for the wheel should be 3.0e5 kg, but I don't understand why.

Thanks in advance! (also, please give suggestions for homework problem format, this is my first)

 

[diazona]

I think they want you to use the formula for the moment of inertia of a disk. That is, don't assume that the mass of the wheel is concentrated around the edge (where the cars are), but instead assume that it's evenly distributed over the whole circle, all the way from the center out to the edge.

 

[quantum13]

Ah, I totally missed that. I still don't understand how you can use the mass divided by two for the equation though.

 

[diazona]

What makes you think you should divide the mass by two?

Why don't you show your new work using the proper formula for moment of inertia of a disk, and we can work from there.