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Minimum Value of Height Change

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A uniform cylinder is allowed to roll down the track. Assume the cylinder rolls without slip, with r_1 = 1.0 m and R_2 = 0.04 m.

What is the minimum value of h such that the cylinder never leaves the surface of the track?
How would the height change if the object is a sphere?

See the attached file.

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The solution determines the minimum value of height change.

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