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• Notes

The masses mi are located at the points pi, Find the moments Mx and My and the center of mass of the system m1 = 6 , m2=5 , m3=10 and P1(1,5), P2(3,-2) , P3(-2,-1).

$M x=\sum_{i=1}^{3} mi y i=m_{1} y_{1}+m_{2} y_{2}+m_{3} y_{3}=(6)(5)+(5)(-2)+(10)(-1)=10$

$M y=\sum_{i=1}^{3} m_{i} x i=m_{1} x_{1}+m_{2} x_{2}+m_{3}x_{3}$

$=(6)(1)+(5)(3)+(10)(-2)=1$

$m=\sum_{i=1}^{3} m i=m_{1}+m_{2}+m_{3}=6+5+10=21$

$\overline{x}=\frac{M y}{m}=\frac{1}{21}$

$\overline{y}=\frac{M x}{m}=\frac{10}{21}$

Center of Mass $(\overline{x}, \overline{y})=\left(\frac{1}{21}, \frac{10}{21}\right)$