A light rope is wrapped several times around a large wheel with a radius of 0.36

Question

A light rope is wrapped several times around a large wheel with a radius of 0.365 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 15.5 kg . The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.90 m/s when it reaches the ground.

Part A Calculate the angular velocity of the wheel when the suitcase reaches the ground. Express your answer in radians per second to three significant figures.

Part B Calculate the moment of inertia of the wheel. Express your answer in kilogram meters squared to three significant figures.

Explanation / Answer

given,

mass = 15.5 kg

height = 4 m

speed = 3.9 m/s

radius = 0.365 m

velocity = angular velocity * radius

3.9 = angular velocity * 0.365

angular velocity = 10.6849 rad/sec

by conservation of energy

initial energy = final energy

mgh = 0.5 * mv^2 + 0.5 * I * w^2

15.5 * 9.8 * 4 = 0.5 * 15.5 * 3.9^2 + 0.5 * I * 10.6849^2

I = 8.579 kg.m^2

moment of inertia = 8.579 kg.m^2

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