Consider a bicycle wheel that initially is not rotating. A block of mass $m$ is attached to the wheel via a string and is allowed to fall a distance $h.$ Assume that the wheel has a moment of inertia I about its rotation axis.

Part A

Consider the case that the string tied to the block is wrapped around the outside of the wheel, which has a radius $r_A$ as shown in $($Figure $1).$ Find ${}_A,$ the angular speed of the wheel after the block has fallen a distance $h,$ for this case.

Express ${}_A$ in terms of $m,g,h,r_A,$ and I.

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