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Conclusion

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I had initially thought that 0.000013 kg*m^2 was a tiny number for the moment of inertia of a yo-yo, however, after further research, the number is surprisingly reasonable.

While little research is done on the moment of inertia of a yo-yo, this website helped a to put things into scope.

http://tutor-homework.com/Physics_Help/yo-yo_speed_inertia.html

The site offers a simulation of a yo-yo that allows you to adjust the numbers as necessary and the moment of inertia is set at a default of 0.000024 kg*m^2 which is fairly close to the moment of inertia I calculated. Although there is no definite way to calculate the actual moment of inertia of the yo-yo without error (even if you did the crazy integrals related to it, the density is not uniform and is for the most part, unknown). I believe I am fairly close to the actual moment of inertia (or at least closer than some of the percent errors I've received on labs in this class).

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