查看“︁重心列表”︁的源代码

{{Copy edit|time=2024-01-12T11:18:53+00:00}}
{| border="2" cellspacing="2" cellpadding="2" 
|- 
! 描述 !! 图形 !! <math>\bar x</math> !! <math>\bar y</math> !! 面积
|-
|'''三角形'''
| align="center" | [[File:Triangle_centroid_1.svg]] [[File:Triangle_centroid_2.svg]]
|<math>\frac{b}{3}</math>
|<math>\frac{h}{3}</math>
|<math>\frac{bh}{2}</math>
|-
|'''四分之一圆'''
| align="center"| [[File:Quarter_circle_centroid.svg]]
|<math>\frac{4r}{3\pi}</math>
|<math>\frac{4r}{3\pi}</math>
|<math>\frac{\pi r^2}{4}</math>
|-
|'''半圆'''
| align="center" | [[File:Semicircle radius 1 centroid.svg]]
|<math>\,\!0</math>
|<math>\frac{4r}{3\pi}</math>
|<math>\frac{\pi r^2}{2}</math>
|-
|'''四分之一椭圆'''
| align="center" | <!-- 檔案不存在 [[File:Elliptical_quarter.svg]] ，可從英文維基百科取得 -->
|<math>\frac{4a}{3\pi}</math>
|<math>\frac{4b}{3\pi}</math>
|<math>\frac{\pi a b}{4}</math>
|-
|'''半椭圆'''
|椭圆<math>\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1</math>与<math>\,\!x</math>轴所围成的图形
|<math>\,\!0</math>
|<math>\frac{4b}{3\pi}</math>
|<math>\frac{\pi a b}{2}</math>
|-
|'''扇形'''
|曲线<math>\,\!r = \rho</math>，直线<math>\,\!\theta = -\alpha</math>与直线<math>\,\!\theta = \alpha</math>所围成的图形
|<math>\frac{2\rho\sin(\alpha)}{3\alpha}</math>
|<math>\,\!0</math>
|<math>\,\!\alpha \rho^2</math>
|-
|'''四分之一圆弧'''
|第一象限内的曲线<math>\,\!x^2 + y^2 = r^2</math>
|<math>\frac{2r}{\pi}</math>
|<math>\frac{2r}{\pi}</math>
|<math>\frac{\pi r}{2}</math>
|-
|'''半圆弧'''
|<math>\,\!x</math>轴上方的曲线<math>\,\!x^2 + y^2 = r^2</math> 
|<math>\,\!0</math>
|<math>\frac{2r}{\pi}</math>
|<math>\,\!\pi r</math>
|-
|'''圆弧'''
|从<math>\,\!\theta = -\alpha</math>到<math>\,\!\theta = \alpha</math>的曲线<math>\,\!r = \rho</math>
|<math>\frac{\rho\sin(\alpha)}{\alpha}</math>
|<math>\,\!0</math>
|<math>\,\!2\alpha \rho</math>
|}

==参见==

* [[几何中心|重心]]

==外部链接==

* [http://www.engineering.com/content/ContentDisplay?contentId=41005016 Centroids of Common Shapes]{{Wayback|url=http://www.engineering.com/content/ContentDisplay?contentId=41005016|date=20061111075125}}
* [http://www.efunda.com/math/areas/IndexArea.cfm Engineering Fundamentals: Common shapes and there properties the invole area..]{{Wayback|url=http://www.efunda.com/math/areas/IndexArea.cfm|date=20210417161736}}
[[Category:经典力学]]
[[Category:物理学列表]]