1. Moment of Inertia
EF Week 15

2. Terminology Moment of inertia = second mass moment
Instead of multiplying mass by distance to the first power (which gives the first mass moment), we multiply it by distance to the second power.

3. Definitions Moment of inertia of a mass, m, about the x axis:
Moment of inertia of a mass, m, about the y axis:
Moment of inertia of a mass, m, about the z axis:

4. Transfer Theorem - 1
We can “transfer” the moment of inertia from one axis to another, provided that the two axes are parallel.
In other words, if we know the moment of inertia about one axis, we can compute it about any other axis parallel to the first axis.

5. Transfer Theorem - 2
If the moment of inertia of a mass m about an axis x’ through the mass center is IGx’, and the distance from the x’ axis to the (parallel) axis x is dy, then the moment of inertia of the mass about the x axis is

6. Transfer Theorem - 3
The moment of inertia to which the transfer term is added is always the one for an axis through the mass center.
The moment of inertia about an axis through the mass center is smaller than the moment of inertia about any other parallel axis.

7. Transfer Theorem - 4
We can transfer from any axis to a parallel axis through the mass center by subtracting the transfer term.

8. Radius of Gyration
By definition, the radius of gyration of a mass m about the x axis is
Given the mass and the radius of gyration,

9. Composite Masses
Since the moment of inertia is an integral, and since the integral over a sum of several masses equals the sum of the integrals over the individual masses, we can find the moment inertia of a composite mass by adding the moments of inertia of its parts.

10. Rods weigh 3 lb/ft. Find IA.

11. Density is 200 kg/m3. Find Iz.

12. Rod: 3 kg/m
Plate: 12 kg/m2
Find IG.