Finding rotational inertia of a yo-yo

AI Thread Summary
To find the rotational inertia of the yo-yo device, apply Newton's second law to both the yo-yo and the box. The system involves a 30 kg box experiencing an upward acceleration of 0.80 m/s² due to a 140 N force applied to a rope around the yo-yo's outer radius of 0.50 m. The hub radius is 0.20 m, which is crucial for calculating the torque and angular acceleration. By integrating these forces and accelerations, the rotational inertia can be determined. This approach effectively utilizes the given parameters to solve the problem.
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A yo-yo shaped device mounted on a horizontal frictionless axis is used to lift a 30kg as shown. The outer radius R of the device is 0.50m, and the radius r of the hub is 0.20 m. Wen a constant horizontal force F of magnitude 140N is applied to a rope wrapped around the outside of the device, the box, which is suspended from arope wrapped around the hub, has an upward acceleration of magnitude 0.80 m/s^2. What is the rotational inertia of the device about its axis of rotation?

http://img438.imageshack.us/img438/7076/problemci9.jpg
 
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Well... where's your work?

Hint: Apply Newton's 2nd law to both the yo-yo and the box. Take advantage of the information given and you'll be able to solve for the rotational inertia.
 

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