So I knew (moment of inertia)*(angular acceleration) = Torque. So I set that equal to (mass of the yo-yo)*(linear acceleration)*(the average radius of the string wrapped around the yo-yo).

I solved for the angular acceleration by taking the final rotational velocity over the time of the throw (the initial velocity is 0, so it is not included). However, rotational velocity is not measured in meters per second, but rather radians per second. In order to find the rotational velocity, I had to divide the velocity I received in the graphs by the radius of the point about the axis of rotation. So (16.85m/s) / (.02781m) = 605.897 rad/s. The time of the throw obtained in the linear acceleration analysis was .26 seconds, so the angular acceleration of the yo-yo turned out to be 2330.37 rad/s/s.

The mass of the yo-yo, linear acceleration, and radius of the string were all either previously known, or calculated through data analysis. The mass is .064 kg. The acceleration is 25.31 m/s/s. And the radius is 0.005 m.

With some simple substitution and algebra, I was able to calculate the moment of inertia of the yo-yo to be 0.000013 kg*m^2.