Kinetic energy of compound rotational objects

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To calculate the kinetic energy of a compound rotational object like a ferris wheel, the moment of inertia for each component must be determined using the appropriate formulas, such as (0.5)mr^2 for rings and disks. The moment of inertia for the shaft can be found using the formula for a cylinder, and all individual moments of inertia should be summed up. Angular velocity is uniform across the entire structure if the components are fixed together, so only one angular velocity value is needed for the entire system. For mechanical energy efficiency, converting kinetic energy to watts requires a time factor, which can be challenging since the energy is constant; thus, proving no mechanical energy efficiency may involve demonstrating that energy input equals output over time. Understanding these principles is crucial for accurately analyzing the kinetic energy and efficiency of rotational systems.
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I have built a ferris wheel out of three parts, a tambourine ring, the cover that came with the tambourine, and a wooden shaft on the other side. I know that to find the kinetic energy would be Iw^2 but I don't really understand how to input the data into the equation.

I know I need to find each individual pieces' moment of inertia, using (0.5)mr^2, (0.5)m(r1^2 +r2^2). I don't know how to find the shaft's moment of inertia though...

And for the angular velocity, do you need to find each pieces separate angular velocity and add them together or do you just need it once because they would all be the same...?

See, I tried finding the answer using just the moment of inertia of the ring and the thin disk (cover) but I got a very very small number...
 
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Find the moment of inertia for each part seperately, through the same axis (!) and add them up.
The angular velocity is the same everywhere on the object (as long as everything is fixed and cannot move relative to each other).

Also, the rotational energy is \frac{1}{2}I \omega^2.
 
thank you!

Last question... I think.
How do you find the mechanical energy efficiency of the whole thing? I'm a little confused as to how to convert the kinetic energy the wheel has into watts. I don't know what the time would be, because essentially the energy is constant.
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I know the end result is that there is no mechanical energy efficiency but I don't know how to find the time so as to prove that there is no energy efficiency...
 
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