Moments of Inertia

There are some posts in this series that remain incomplete. Unfortunately, I just got busy. But 90% of the content is here, and I have spent a ridiculous amount of time on this. At some point you just have to publish a draft. I have noted when content is missing. I promise to come back to this and touch up the last 10% in the future.


0) Introduction

Theory and Background

1) Definition of the Mass Moment of Inertia
2) Inertia Tensor Derivation
3) Coordinate Systems
4) Vector Integration
5) Parallel Axis Theorem
6) Principal Axis Theorem
7) Intermediate Axis Theorem

Curves

8) Lines
9) Lines in the XY Plane
10) Triangle
11) Rectangle
12) Polygon
13) Circle
14) Ellipse (Impossible)

Surfaces

15) Rectangle
16) Triangle
17) Polygon
18) Circular Disc
19) Elliptical Disc
20) Hoop (Cylindrical Shell)
21) Spherical Shell
22) Elliptical Shell (Impossible)

Volumes

23) Rod (Solid Cylinder)
24) Rectangular Slab
25) Spherical Ball
26) Ellipsoid
27) Cone
28) Torus
29) Ring (Annular Cylinder)