A yo-yo-shaped device mounted on a horizontal frictionless axis is used to lift a \(30 \mathrm{~....

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A yo-yo-shaped device mounted on a horizontal frictionless axis is used to lift a \(30 \mathrm{~kg}\) box as shown in figure. The outer radius \(R\) of the device is \(0.50 \mathrm{~m}\), and the radius \(r\) of the hub is \(0.20 \mathrm{~m}\). When a constant horizontal force of magnitude \(152 \mathrm{~N}\) is applied in the left direction to a rope wrapped around the outside of the device, the box, which is suspended from a rope wrapped around the hub, has an upward acceleration of magnitude \(0.80 \mathrm{~m} / \mathrm{s}^{2}\). What is the rotational inertia \(I\) (in \(\mathrm{kg}-\mathrm{m}^{2}\) ) of the device about its axis of rotation?
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