Chapter 10, Problem 098 A yo-yo-shaped device mounted on a horizontal frictionle

Question

Chapter 10, Problem 098 A yo-yo-shaped device mounted on a horizontal frictionless axis is used to lift a 27 kg box as shown in the figure. The outer radius R of the device is 0.89 m, and the radius r of the hub is 0.40 m. When a constar horizontal force app of magnitude 180 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 0.74 m/s2. What is the rotational inertia of the device about its axis of rotation? Rigid mount Hub Yoyo shapedo Rope device

Explanation / Answer

on mass:

T - m g = m a

T = 27 (9.81 + 0.74) = 284.85 N

on device,

net torque = I alpha

(180 x 0.89) - (284.85 x 0.40) = I (0.74 / 0.40)

I = 25 kg m^2 ..........Ans

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