Vlad needs to draw water from a deep well. He is using a bucket that is connected by rope (negligible mass) to a wooden axle at the top of the well. By cranking a handle at the end of the axle, Vlad is able to unwind the rope around the axle and move the bucket downward. The radius of the axle is R = 30 cm. The bucket is traveling downward at speed vi = 25 cm/s when the handle slips out of Vlad’s hand. As the rope unwinds and the bucket falls downward, the axle spins freely with an angular acceleration whose magnitude is α = 4.5 rad/s^2. The bucket falls through a distance of d = 7.0 m before crashing into the water. 1. What is the angular speed ωf of the axle when the bucket first hits the water?  2. As d → 0, what limit does ωf approach and why?

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Vlad needs to draw water from a deep well. He is using a bucket that is connected by rope (negligible mass) to a wooden axle at the top of the well. By cranking a handle at the end of the axle, Vlad is able to unwind the rope around the axle and move the bucket downward. The radius of the axle is R = 30 cm. The bucket is traveling downward at speed vi = 25 cm/s when the handle slips out of Vlad’s hand. As the rope unwinds and the bucket falls downward, the axle spins freely with an angular acceleration whose magnitude is α = 4.5 rad/s^2. The bucket falls through a distance of d = 7.0 m before crashing into the water.

1. What is the angular speed ωf of the axle when the bucket first hits the water? 

2. As d → 0, what limit does ωf approach and why?

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