${\displaystyle {\begin{array}{l}{\vec {P}}=-mg\,{\vec {\jmath }}\\{\vec {\Phi }}_{1\to 2}^{\,O}=O_{x}\,{\vec {\imath }}+O_{y}\,{\vec {\jmath }}+O_{z}\,{\vec {k}}\\{\vec {\tau }}=\tau _{0}\,{\vec {k}}\end{array}}}$

${\displaystyle {\vec {P}}+{\vec {\Phi }}_{1\to 2}^{\,O}={\vec {0}}\Longrightarrow \left\{{\begin{array}{lclr}(X)&\to &O_{x}=0&(1)\\(Y)&\to &O_{y}=mg&(2)\\(Z)&\to &O_{z}=0&(3)\end{array}}\right.}$

${\displaystyle {\vec {M}}_{O}={\vec {\tau }}+{\overrightarrow {OG_{2}}}\times {\vec {P}}={\vec {0}}}$

${\displaystyle {\overrightarrow {OG_{2}}}\times {\vec {P}}=(L\,\mathrm {sen} \,\theta _{1}\,{\vec {\imath }}+L\cos \theta _{1}\,{\vec {\jmath }})\times (-mg\,{\vec {\jmath }})=-mgL\,\mathrm {sen} \,\theta \,{\vec {k}}}$

${\displaystyle \tau _{0}-mgL\,\mathrm {sen} \,\theta _{1}=0,\qquad \qquad (4)}$

${\displaystyle {\vec {\tau }}=mgL\,\mathrm {sen} \,\theta _{1}\,{\vec {k}}={\dfrac {1}{2}}mgL\,{\vec {k}}}$

${\displaystyle {\begin{array}{l}{\vec {P}}_{2}=-mg\,{\vec {\jmath }}\\{\vec {\Phi }}_{1\to 2}^{\,O}=O_{x}\,{\vec {\imath }}+O_{y}\,{\vec {\jmath }}+O_{z}\,{\vec {k}}\\{\vec {\Phi }}_{0\to 2}^{\,A}=-A_{y}\,{\vec {\jmath }}\\{\vec {\tau }}=\tau _{0}\,{\vec {k}}\end{array}}}$

${\displaystyle {\begin{array}{l}{\vec {P}}_{0}=-mg\,{\vec {\jmath }}\\{\vec {\Phi }}_{2\to 0}^{\,A}=A_{y}\,{\vec {\jmath }}\\{\vec {\Phi }}_{1\to 0}^{\,B}=B_{x}\,{\vec {\imath }}+B_{z}\,{\vec {k}}\\{\vec {\Gamma }}_{1\to 0}=\Gamma \,{\vec {k}}\end{array}}}$

${\displaystyle {\vec {P}}_{2}+{\vec {\Phi }}_{1\to 2}^{\,O}+{\vec {\Phi }}_{0\to 2}^{\,A}={\vec {0}}\Longrightarrow \left\{{\begin{array}{lclr}(X)&\to &O_{x}=0&(1)\\(Y)&\to &O_{y}-A_{y}=mg&(2)\\(Z)&\to &O_{z}=0&(3)\end{array}}\right.}$

${\displaystyle {\vec {M}}_{O}={\vec {\tau }}+{\overrightarrow {OG_{2}}}\times {\vec {P}}_{2}+{\overrightarrow {OA}}\times {\vec {\Phi }}_{0\to 2}^{\,A}={\vec {0}}\Longrightarrow \tau _{0}-mgL\,\mathrm {sen} \,\theta -2A_{y}L\,\mathrm {sen} \,\theta =0\,\qquad (4)}$

${\displaystyle {\vec {P}}_{0}+{\vec {\Phi }}_{1\to 0}^{\,B}+{\vec {\Phi }}_{2\to 0}^{\,A}={\vec {0}}\Longrightarrow \left\{{\begin{array}{lclr}(X)&\to &B_{x}=0&(5)\\(Y)&\to &A_{y}=mg&(6)\\(Z)&\to &B_{z}=0&(7)\end{array}}\right.}$

${\displaystyle {\vec {M}}_{B}={\overrightarrow {BG}}_{0}\times {\vec {P}}_{0}+{\overrightarrow {BA}}\times {\vec {\Phi }}_{2\to 0}^{\,A}+{\vec {\Gamma }}_{1\to 0}={\vec {0}}}$

${\displaystyle {\begin{array}{l}{\overrightarrow {BG}}_{0}\times {\vec {P}}_{0}=(L\,{\vec {\imath }})\times (-mg\,{\vec {\jmath }})=-mgL\,{\vec {k}}\\{\overrightarrow {BA}}\times {\vec {\Phi }}_{2\to 0}^{\,A}=(2L\,\mathrm {sen} \,\theta \,{\vec {\imath }})\times (A_{y}\,{\vec {\jmath }})=2LA_{y}\,\mathrm {sen} \,\theta \,{\vec {k}}\end{array}}}$

${\displaystyle \Gamma -mgL+2LA_{y}\,\mathrm {sen} \,\theta =0.\qquad (8)}$

${\displaystyle {\begin{array}{l}{\vec {\Phi }}_{1\to 2}^{\,O}=2mg\,{\vec {\jmath }},\\{\vec {\Phi }}_{2\to 0}^{\,A}=mg\,{\vec {\jmath }},\\{\vec {\Phi }}_{1\to 0}^{\,B}={\vec {0}}\\\\{\vec {\Gamma }}_{1\to 0}={\dfrac {2}{3}}mgL\,{\vec {k}}\\\mathrm {sen} \,\theta ={\dfrac {\tau _{0}}{3mgL}}={\dfrac {1}{6}}\end{array}}}$