A light rope is wrapped several times around a large wheel with a radius of 0.39

Question

A light rope is wrapped several times around a large wheel with a radius of 0.390 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 20.0 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. (in rad/s)

b) Calculate the moment of inertia of the wheel. (in kgm^2)

Explanation / Answer

part a )

angular velocity = V/r

w = 3.10 / 0.390

w = 7.95 rad/s

part b )

torque = T*r = I*alpha

a = v^2/2s

a = 3.10 x 3.10 / 2*4 = 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 = 21.8 kgm^2

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