# 飛輪

(重新導向自 飛輪 (能量儲存元件))

## 原理

${\displaystyle E_{k}={\frac {1}{2}}\cdot I\cdot \omega ^{2}}$

${\displaystyle \omega }$角速度
${\displaystyle I}$質量相對軸心的轉動慣量，轉動慣量是物體抵抗力矩的能力，給予一定力矩，轉動慣量越大的物體轉速越低。
• 固體圓柱的轉動慣量為${\displaystyle I_{z}={\frac {1}{2}}mr^{2}}$,
• 若是薄壁空心圓柱，轉動慣量為${\displaystyle I=mr^{2}\,}$,
• 若是厚壁空心圓柱，轉動慣量則為${\displaystyle I={\frac {1}{2}}m({r_{1}}^{2}+{r_{2}}^{2})}$.

${\displaystyle \sigma _{t}=\rho r^{2}\omega ^{2}\ }$

${\displaystyle \sigma _{t}}$是轉子外圈所受到的張應力
${\displaystyle \rho }$是轉子的密度
${\displaystyle r}$是轉子的半徑
${\displaystyle \omega }$是轉子的角速度

## 飛輪儲存的能量

### 飛輪能量和材料的關係

${\displaystyle E_{k}\varpropto \sigma _{t}V}$

${\displaystyle E_{k}\varpropto {\frac {\sigma _{t}}{\rho }}m}$

${\displaystyle {\frac {\sigma _{t}}{\rho }}}$可以稱為比強度。若飛輪使用材質的比強度越高，其單位質量下的能量密度也就就越大。

## 參考

1. ^ 邱映輝. 機械設計. 北京: 清華大學出版社. 2004: 187 [2010-07-16]. 7302094020.
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4. White, Jr., Lynn. Theophilus Redivivus. Technology and Culture. Spring 1964, 5 (2): 233.
5. ^ Ahmad Y Hassan. Flywheel Effect for a Saqiya. History of Science and Technology in Islam. [2010-07-14]. （原始內容存檔於2010-10-07）.
6. ^ White, Jr., Lynn. Medieval Engineering and the Sociology of Knowledge. The Pacific Historical Review. Feb 1975, 44 (1): 6.
1. ^ 1/(60 * 24)*(366.26/365.26)