A light rope is wrapped several times around a large wheel with a radius of 0.35

Question

A light rope is wrapped several times around a large wheel with a radius of 0.355m . 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 18.5kg . The suitcase is released from rest at a height of 4.00m above the ground. The suitcase has a speed of 3.65m/s when it reaches the ground.

Part A

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

  rad/s

Part B

Calculate the moment of inertia of the wheel.

  rad/s

Explanation / Answer

the total of KE and PE at the beginning and the end are equal
at the beginning you have only the GPE of the suitcase
at the end that GPE is reduced to zero and the suitcase and the wheel have a total KE
so
m g h = 1/2 m v^2 + 1/2 I ?2
we need ?
? = v/r where v is tangential speed of wheel rim which is the same as the linear v of the suitcase
? = 3.65/0.355 = .. rad/s
so
18.5 (9.81) (4.00) = 1/2 (18.5) (3.65)^2 + 1/2 I (w)^2

I = ............ kg*m^2

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