1. At the vertices of the quadrilateral $A_{1} A_{2} A_{3} A_{4}$ (Fig. 62), the following masses are placed: $2, 6, 2, 3$. Calculate the moment of inertia of the resulting system of material points relative to the point $S$. (The side of each square on Fig. 62 is 1 unit.) (O. 117, P. 177.)

![](https://cdn.mathpix.com/cropped/2024_05_21_27f86caa754616304e40g-072.jpg?height=501&width=402&top_left_y=1007&top_left_x=699)

Fig. 62.
1. The sought moment of inertia is

$$
\begin{aligned}
J_{S}=2 \cdot S A_{1}^{2} & +6 \cdot S A_{2}^{2}+2 \cdot S A_{3}^{2}+3 \cdot S A_{4}^{2}= \\
& =2\left(3^{2}+4^{2}\right)+6 \cdot 2^{2}+2\left(3^{2}+4^{2}\right)+3 \cdot 8^{2}=316
\end{aligned}
$$