A yo-yo-shaped device mounted on a horizontal frictionless axis is used to lift a 30 kg box as shown in figure. The outer radius R of the device is 0.50 m, an the radius r of the hub is 0.20 m. When a constant horizontal force of magnitude 152 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 m / s 2. What is the rotational inertia I (in k g-m2 ) of the device about its axis of rotation?

Question

A yo-yo-shaped device mounted on a horizontal frictionless axis is used to lift a 30 kg box as shown in figure. The outer radius R of the device is 0.50 m, an the radius r of the hub is 0.20 m. When a constant horizontal force of magnitude 152 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 m / s 2. What is the rotational inertia I (in k g-m2 ) of the device about its axis of rotation? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

152 × 0.5- T × 0.2= I α T -300=0.8 × 30 T =324 76-324 × 0.2= I α 0.2 α=0.8 α=4 11.2= I × 4 I =2.8 kg - m 2

152×0.5−T×0.2=Iα T−300=0.8×30 T=324 76−324×0.2=Iα 0.2α=0.8 α=4 11.2=I×4 I=2.8kg−m2

$152 \times 0.5 - T \times 0.2 = I α$
$T - 300 = 0.8 \times 30$
$T = 324$
$76 - 324 \times 0.2 = I α$
$0.2 α = 0.8$
$α = 4$
$11.2 = I \times 4$
$I = 2.8 k g - m^{2}$