91影视

lumina$惟$composed ofn non-overlapping lamin忙 ${惟}_1,{惟}_2,鈥�,{惟}_n.$

masses of lumina role="math" localid="1650321740246" ${惟}_1,{惟}_2,鈥�,{惟}_n$are $m_1,m_2,鈥�,m_n$with a center of masses at $\left({\stackrel{炉}{x}}_1,{\stackrel{炉}{y}}_1\right),\left({\stackrel{炉}{x}}_2,{\stackrel{炉}{y}}_2\right),鈥�,\left({\stackrel{炉}{x}}_n,{\stackrel{炉}{y}}_n\right).$

center of mass of$惟$is$\stackrel{炉}{x}=\frac{{鈭�}_{k=1}^n{m}_k{\stackrel{炉}{x}}_k}{{鈭�}_{k=1}^n{m}_k}\text{and}\stackrel{炉}{y}=\frac{{鈭�}_{k=1}^n{m}_k{\stackrel{炉}{y}}_k}{{鈭�}_{k=1}^n{m}_k}.$

The x-coordinate of the center $\overline{x}$of mass of ${惟}_1$is role="math" localid="1650322246084" $\overline{x}=\frac{M_y}{m_1}$

So linear moment of the mass about the y-axis of ${惟}_1$is $M_y=m_1\overline{x}$

similarly, a linear moment of the mass about the y-axis of ${惟}_2,{惟}_3,鈥�,{惟}_n$are following.

$$\begin{gathered} M_y=m_2\overline{x} \\ {M}_y=m_3\overline{x} \\ 鈰� \\ {M}_y=m_n\overline{x} \end{gathered}$$

The y-coordinate of the center of mass $\overline{y}$of ${惟}_2$is $\overline{y}=\frac{M_y}{m_2}$

So linear moment of the mass about the x-axis of ${惟}_1$is $M_x=m_1\overline{y}$

similarly, a linear moment of the mass about the x-axis of ${惟}_2,{惟}_3,鈥�,{惟}_n$are following.

$$\begin{gathered} M_x=m_2\overline{y} \\ {M}_x=m_3\overline{y} \\ 鈰� \\ {M}_x=m_n\overline{y} \end{gathered}$$

center of mass $\overline{x}$is the ratio of the sum of all linear moments of the mass about the y-axis to the sum of all masses.

role="math" localid="1650322903342" $$\begin{gathered} \stackrel{炉}{x}=\frac{m_1{\stackrel{炉}{x}}_1+m_2{\stackrel{炉}{x}}_2+鈰�+m_n{\stackrel{炉}{x}}_n}{m_1+m_2+鈰�+m_n} \\ \stackrel{炉}{x}=\frac{{鈭�}_{k=1}^n{m}_k{\stackrel{炉}{x}}_k}{{鈭�}_{k=1}^n{m}_k} \end{gathered}$$

center of mass $\overline{y}$is the ratio of the sum of all linear moments of the mass about the x-axis to the sum of all masses.

role="math" localid="1650322895845" $$\begin{gathered} \stackrel{炉}{y}=\frac{m_1{\stackrel{炉}{y}}_1+m_2{\stackrel{炉}{y}}_2+鈰�+m_n{\stackrel{炉}{y}}_n}{m_1+m_2+鈰�+m_n} \\ \stackrel{炉}{y}=\frac{{鈭�}_{k=1}^n{m}_k{\stackrel{炉}{y}}_k}{{鈭�}_{k=1}^n{m}_k} \end{gathered}$$

So the center of mass of $惟$is$\stackrel{炉}{x}=\frac{{鈭�}_{k=1}^n{m}_k{\stackrel{炉}{x}}_k}{{鈭�}_{k=1}^n{m}_k}\text{and}\stackrel{炉}{y}=\frac{{鈭�}_{k=1}^n{m}_k{\stackrel{炉}{y}}_k}{{鈭�}_{k=1}^n{m}_k}.$