A thin light string is wrapped around the outer rim of a uniform hollow cylinder of mass $4\mathrm{.}55$ kg having inner and outer radii as shown in the figure $($Figure $1).$ The cylinder is then released from rest.

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Part A

How far must the cylinder fall before its center is moving at $6\mathrm{.}16\frac{m}{s}?$

Express your answer in meters.

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Part B

If you just dropped this cylinder without any string, how fast would its center be moving when it had fallen the distance in part A$?$

Express your answer in meters per second.

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Figure

$1$ of $1$