A light rope is wrapped several times around a large wheel with a radius of 0.43

Question

A light rope is wrapped several times around a large wheel with a radius of 0.435m . 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 3.20m/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. I =

Explanation / Answer

A) Apply, linear speed on the tip, v = R*w (R is radius and w is angular speed)

==> w = v/R

= 3.2/0.435

= 7.36 rad/s

B) Apply energy conservation

Initial mechanical enrgy = final mechaincal energy.

m*g*H = 0.5*m*v^2 + 0.5*I*w^2

20*9.8*4 = 0.5*20*3.2^2 + 0.5*I*7.36^2

==> I = (20*9.8*4 - 0.5*20*3.2^2)/(0.5*7.36^2)

= 25.17 kg.m^2 <<<<<<<<--------Answer

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