A light rope is wrapped several times around a large wheel with a radius of 0.41

Question

A light rope is wrapped several times around a large wheel with a radius of 0.410 m . The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure (Figure 1) . The free end of the rope is tied to a suitcase with a mass of 19.0 kg . The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.10 m/s when it reaches the ground.

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

b.) Calculate the moment of inertia of the wheel.

Explanation / Answer

part a ) from V = rW

angular velocity W = V/r

w = 3.10 / 0.41

w = 7.56 rad/s

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part b ) use the formua torque = T*r = I*alpha

a = v^2/2s

a = 3.10 x 3.10 / 2*4

a = 1.20 m/s^2

now force on suitcase

mg - T = ma

T = mg-ma

torque = (mg -ma)*r = I*alpha

alpha = a/r

(mg - ma )r^2/a = I

I = (19 *(9.8 -1.2) * 0.41* 0.41/1.2

I = MOI = 22.88 kgm^2

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