# 飛輪

（重定向自飞轮

## 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

## 飞轮儲存的能量

### 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

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4. White, Jr., Lynn. Theophilus Redivivus. Technology and Culture. Spring 1964, 5 (2): 233.
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6. ^ White, Jr., Lynn. Medieval Engineering and the Sociology of Knowledge. The Pacific Historical Review. Feb 1975, 44 (1): 6.
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