The force \(P\), which is applied to the cable wrapped around the central hub of the symmetrical wheel, is increased slowly according to \(P=1.5 t\), where \(P\) is in pounds and \(t\) is the time in seconds after \(P\) is first applied. Determine the angular velocity \(\omega_{2}\) of the wheel 10 seconds after \(P\) is applied if the wheel is rolling to the left with a velocity of its center of \(3 \mathrm{ft} / \mathrm{sec}\) at time \(t=0\). The wheel weighs \(120 \mathrm{lb}\) with a radius of gyration about its center of \(10 \mathrm{in}\). and rolls without slipping.

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18" 9" V = 3 ft/sec/ |G P