Chapter 10. Moments of Inertia
Lecture 2/2
EGM 3512: Engineering Mechanics
Instructor: Sungmoon Jung (sjung@eng.fsu.edu)
Lecture 1/2 Summary
•  Definition of the moment of inertia
▫  Do not memorize the eq., but understand “second
moment of the area”
Lecture 1/2 Summary (Continued)
•  Parallel-axis theorem
▫  When the axis does not pass the centroid, the second
moment of the entire area has to be added
Lecture 1/2 Summary (Continued)
•  Make it sure that you know how to compute the moment
of inertia using integration
What We Need to Learn in Lecture 2/2
•  Definition of the moment of inertia
•  Parallel axis theorem
•  To calculate the moment of inertia
▫  Single area using integration
▫  Composite areas using table
•  Mass moment of inertia
What We Need to Learn
•  Definition of the moment of inertia
•  Parallel axis theorem
•  To calculate the moment of inertia
▫  Single area using integration
▫  Composite areas using table
•  Mass moment of inertia
Moment of Inertia of Composite Areas
(About a Given Axis)
Moment of inertia
of a complex area
Break into simpler
shapes, then compute
moment of inertia of
them (using the table)
=
Add (or subtract)
m.o.i. of simple
shapes
=
Example 1
•  Compute the moment of inertia about x-axis
During the test, the following will be given.
Example 2
•  Compute the moment of inertia about x-axis and y-axis
Moment of Inertia of Composite Areas
(About an Axis that Passes the Centroid)
•  We often have to first find the centroid, and then
compute the moment of inertia about an axis that passes
the centroid
•  The main procedure is the same. Just be sure to compute
the centroid first.
Example 3
•  Determine the location of the centroid (y), then compute
the moment of inertia about x’ axis
What We Need to Learn
•  Definition of the moment of inertia
•  Parallel axis theorem
•  To calculate the moment of inertia
▫  Single area using integration
▫  Composite areas using table
•  Mass moment of inertia
Mass Moment of Inertia
•  Definition
Moment of inertia: second moment of the area about an axis
Mass moment of inertia: second moment of the (
) about an axis
Mass Moment of Inertia (Continued)
•  Parallel-axis theorem
What We Learned in This Lecture
•  Definition of the moment of inertia
•  Parallel axis theorem
•  To calculate the moment of inertia
▫  Single area using integration
▫  Composite areas using table
•  Mass moment of inertia
The class has not finished yet.
Review the PowerPoint slides, then
take the quiz in the Blackboard.