The wheel rolls up the incline on its hubs without slipping and is pulled by the \(100-\mathrm{N}\) force applied to the cord wrapped around its outer rim. If the wheel starts from rest, compute its angular velocity \(\omega\) after its center has moved a distance of \(3 \mathrm{~m}\) up the incline. The wheel has a mass of \(40 \mathrm{~kg}\) with center of mass at \(O\) and has a centroidal radius of gyration of \(150 \mathrm{~mm}\). Determine the power input from the \(100-\mathrm{N}\) force at the end of the \(3-\mathrm{m}\) motion interval.

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200 mm 100 N 100 mm 15