A yo-yo-shapeddevice mounted on a horizontal frictionless axis is used to lift a

Question

A yo-yo-shapeddevice mounted on a horizontal frictionless axis is used to lift a23 kg box as shown in Fig. 10-59. The outer radius R of the deviceis 0.48 m, and the radius r of the hub is 0.22 m. When a constanthorizontal force of magnitude Fapp = 144 N is applied to a ropewrapped around the outside of the device, the box, which issuspended from a rope wrapped around the hub, has un upwardacceleration of magnitude 0.76 m/s2.
What is the rotational inertia of the device about its axis ofrotation?            kg·m2

Explanation / Answer

   in the given problem let us assume that T astension on the rope    from the newtons second law of motion weget    T - m g = m a    T = m (g + a)    since the box has an upward acceleration athe tension is given by    T = (23 kg) (9.80 + 0.76)       = ....... N    the rotation of the device is desribedby    Fapp R - T r = I                        =I a / r    the moment of inertia will be    I = r (Fapp R - T r) / a      = ......... kg . m2

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