(Solved): The object shown is in rotational equilibrium. Which equation represents the sum of the torques ac ...

The object shown is in rotational equilibrium. Which equation represents the sum of the torques acting on this object? Assume the axis is through point \( O \). (i) \[ \begin{array}{l} F_{y}\left(\frac{\ell}{2}\right) \cos \theta-R_{y}\left(\frac{\ell}{2}\right) \cos \theta-F_{x}\left(\frac{\ell}{2}\right) \sin \theta+R_{x}\left(\frac{\ell}{2}\right) \sin \theta=0 \\ F_{x}-R_{x}=0 \\ F_{y}+R_{y}-F_{g}=0 \\ F_{y} \ell \cos \theta-F_{g}\left(\frac{\ell}{2}\right) \cos \theta-F_{x} \ell \sin \theta=0 \\ F_{x}+F_{y}=0 \\ R_{x}+R_{y}=0 \end{array} \]