As an intern at an engineering firm, you are asked to measure the moment of inertia of a large wheel for rotation about an axis perpendicular to the wheel at its center. You measure the diameter of the wheel to be $0\mathrm{.}520m.$ Then you mount the wheel on frictionless bearings on a horizontal frictionless axle at the center of the wheel. You wrap a light rope around the wheel and hang an $8\mathrm{.}20kg$ block of wood from the free end of the rope, as in$.$ You

release the system from rest and find that the block descends $12\mathrm{.}0m$ in $4\mathrm{.}00s.$

Part A

What is the moment of inertia of the wheel for this axis?

Express your answer with the appropriate units.