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 0.410m . 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 20.0kg . The suitcase is released from rest at a height of 4.00m above the ground. The suitcase has a speed of 3.75m/s when it reaches the ground.

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

Part B) Calculate the moment of inertia of the wheel

Explanation / Answer

Torque = T*R = I*? = I*a/R

where T = tension is (mg - ma) with m = mass of the suitcase, a is the linear acceleration.

the linear acceleration is found from
v = ?(2as)
v^2 = 2as
a = v^2/(2s)
a = 3.75^2/(2*4)
a = 1.75 m/s^2

put into equation
(mg - ma)R = I*a/R
I = (mg - ma)*R^2/a
I = (20*9.81 - 20*1.75)*0.410^2/1.75
I = 15.45 kg m^2 <--- ans

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