17: Appendix 2 - Moment Integrals
- Page ID
- 55336
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
- 17.1: Moment Integrals
- Overview of moment integrals: the general concept of using integration to determine the net moment of a force that is spread over an area or volume.
- 17.2: Centroids of Areas via Integration
- Procedure for finding the location of the centroid of a two-dimensional shape, by taking the first moment integral.
- 17.3: Centroids in Volumes and Center of Mass via Integration
- Procedure to find the location of the centroid of a three-dimensional volume and to find the center of mass of a volume of non-uniform density, by taking the first moment integral.
- 17.4: Centroids and Centers of Mass via Method of Composite Parts
- Procedure to find the location of the centroid/center of mass of a shape by the Method of Composite Parts: breaking the shape down into simpler components for individual analysis.
- 17.5: Area Moments of Inertia via Integration
- Procedure for finding a body's area moments of inertia through integration, used to determine the body's resistance to bending (second area moments) or resistance to torsion (polar moment of inertia).
- 17.6: Mass Moments of Inertia via Integration
- Procedure for finding an object's mass moment of inertia, or resistance to rotation about an axis, through integration.
- 17.7: Moments of Inertia via Composite Parts and Parallel Axis Theorem
- Calculating moments of inertia via the Method of Composite Parts, as an alternative to integration.