# 力偶

## 簡單力偶

${\displaystyle \tau =Fd\,}$

${\displaystyle \mathbf {F} _{1}+\mathbf {F} _{2}=0\,}$

${\displaystyle \mathbf {M} =\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}=\mathbf {r} _{12}\times \mathbf {F} _{1}\,}$

## 力偶矩與參考點無關

${\displaystyle \mathbf {F} _{1}+\mathbf {F} _{2}=0\,}$

${\displaystyle \mathbf {M} _{O}=\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}\,}$

${\displaystyle \mathbf {M} _{P}=(\mathbf {r} _{1}-\mathbf {r} )\times \mathbf {F} _{1}+(\mathbf {r} _{2}-\mathbf {r} )\times \mathbf {F} _{2}=\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}-\mathbf {r} \times (\mathbf {F} _{1}+\mathbf {F} _{2})=\mathbf {r} _{1}\times \mathbf {F} _{1}+\mathbf {r} _{2}\times \mathbf {F} _{2}\,}$

${\displaystyle \mathbf {M} _{P}=\mathbf {M} _{O}\,}$

## 參考文獻

1. Dynamics, Theory and Applications by T.R. Kane and D.A. Levinson, 1985, pp. 90-99: 自由下載页面存档备份，存于互联网档案馆
2. ^ Physics for Engineering by Hendricks, Subramony, and Van Blerk, page 148
3. ^ Engineering Mechanics: Equilibrium, by C. Hartsuijker, J. W. Welleman, page 64