The document summarizes key concepts relating to area moment of inertia including that it represents the second moment of area about an axis and is used in structural strength equations. It can be determined by integration for irregular shapes or found in tables for common shapes. The parallel axis theorem allows calculating it about other axes or for composite shapes. Product of inertia and principal moments of inertia can also be determined using formulas, Mohr's circle, or the parallel axis theorem. Mass moment of inertia measures rotational resistance and can be found using disk or shell elements for axially symmetric bodies.

1. Chapter Summary
Area Moment of Inertia
Represent second moment of area about an axis
Frequently used in equations related to strength
and stability of structural members or mechanical
elements
If the area shape is irregular, a differential
element must be selected and integration over
the entire area must be performed
Tabular values of the moment of inertia of
common shapes about their centroidal axis are
available

2. Chapter Summary
Area Moment of Inertia
To determine moment of inertia of these shapes
about some other axis, parallel axis theorem
must be used
If an area is a composite of these shapes, its
moment of inertia = sum of the moments of
inertia of each of its parts
Product of Inertia
Determine location of an axis about which the
moment of inertia for the area is a maximum or
minimum

3. Chapter Summary
Product of Inertia
If the product of inertia for an area is known
about its x’, y’ axes, then its value can be
determined about any x, y axes using the parallel
axis theorem for product of inertia
Principal Moments of Inertia
Provided moments of inertia are known, formulas
or Mohr’s circle can be used to determine the
maximum or minimum or principal moments of
inertia for the area, as well as orientation of the
principal axes of inertia

4. Chapter Summary
Mass Moments of Inertia
Measures resistance to change in its rotation
Second moment of the mass elements of the
body about an axis
For bodies having axial symmetry, determine
using wither disk or shell elements
Mass moment of inertia of a composite body is
determined using tabular values of its composite
shapes along with the parallel axis theorem

5. Chapter Review

6. Chapter Review

7. Chapter Review

8. Chapter Review