## Answers

Calculate your Inertiak_{G} = 2ftk_{G} = √(I_{G}/m)I_{G} = (m)(k_{G}^{2})I_{G} = (500/32.2)(2^{2})I_{G} = 62.11 lb ft^{2}|Sum your forces:ΣF_{x} = m(a_{G})_{x}F_{A} =(500/32.2)(a_{G})_{x}ΣF_{y} = m(a_{G})_{y}N_{a} - 500 = 0ΣM_{G} =(I_{G})(α_{G})-(F_{A})(3) =(62.11)(α_{G})|No slipping thereforea_{G/T} = αra_{G/T} = 3α|The acceleration of the spoolis relative to that of thetrucka_{G} = a_{T} + a_{G/T}a_{G} =(3 ft/s^{2})+ 3α|SolveyourΣF_{x}&ΣM_{G}simultaneously to find α_{G}F_{A} = (500/32.2)(a_{G})_{x}-(F_{A})(3) = (62.11)(α_{G})|F_{A} = (500/32.2)(3 + 3α)-(F_{A})(3) = (62.11)(α)|F_{A} = (500/32.2)(3 + 3α)-F_{A} = 20.70α|0= 46.584 + 67.287αα = -0.692α = 0.692 rotating counterclockwise.

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