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Consider the motion of the rock in the figure below. What is the minimum speed the rock can have without the string becoming "slack"? (The rock is traveling in vertical circle. Assume that m = 1.4 kg and r = 0.56 m.)
m/s

A roller coaster track is designed so that the car travels upside down on a certain portion of the track as shown in the figure below. What is the minimum speed the roller coaster can have without falling from the track? Assume the track has a radius of curvature of 28 m.
m/s

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v^2/r= 9.8

In the first case

v^2/0.56= 9.8

v= 2.34 m/s

In the second

v^2/28= 9.8

v= 16.57 m/s
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