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

Question

A yo-yo-shaped device mounted on a horizontal frictionless axis is used to lift a 21-kg box as shown in Fig. 10-59.


Fig. 10-59

The outer radius R of the device is 0.50 m, and the radius r of the hub is 0.20 m. When a constant horizontal force Fapp of magnitude 150 N is applied 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 m/s2 What is the rotational inertia of the device about its axis of rotation?

Explanation / Answer

m = 21-kg, R = 0.50 m, r = 0.20 m. F = 150 N, a = 0.80 m/s^2, find the rotational inertia I of the device about its axis of rotation. tension of the rope connecting the box = T, angular acceleration of yo-yo = alpha = a/r for m: T - mg = ma, so T = m(a + g) = 222.6 N for yo-yo: F*R - T*r = I*alpha = I*a/r so I = (FR - Tr)r/a = 7.62 kgm^2

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