A light rope is wrapped several times around a large wheel with a radius of 0.40

Question

A light rope is wrapped several times around a large wheel with a radius of 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure . The free end of the rope is tied to a suitcase with a mass of 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground.

Calculate the angular velocity of the wheel when the suitcase reaches the ground.

Calculate the moment of inertia of the wheel.

Explanation / Answer

A) w = v/r = (3.50)/(0.400) = 8.75 rad/s B) Ki + Ui = Kf + Uf Ki and Uf = 0 Ui = Kf mgh = 1/2 mv2 + 1/2Iw2 (15)(9.8)(4) = 1/2 (15)(3.5)2 + 1/2 (I) (8.75)2 588 = 91.9 + 38.3(I) 496.1 = 38.3(I) I = 12.9 kgm2

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