# MOMENT OF INERTIA

### RADIUS OF GYRATION:

- The distance from the axis of rotation to a point where all of the mass or area can be concentrated to yield the same resistance to angular motion.

- An averaging out of the radii (r) of all the mass particles. This allows all the mass or area to be represented by a single radius (k).

I = mk² or I = Ak²

- The distribution of an object’s mass has a much The distribution of an object’s mass or area has a much greater affect on the moment of inertia than mass.

### Principal Axes for any Object

**Maximum Moment of Inertia Axis (Imax):** Axis that has the largest moment of inertia.

** Minimum Moment of Inertia Axis (Imin):** Axis that has the smallest moment of inertia.

** Intermediate Moment of Inertia Axis (Iint):** Has an intermediate moment of inertia. Determined not by its moment of inertia value, but rather because it is perpendicular to the both Imax and Imin. Note: All three axes are perpendicular to each other

**Note:** All three axes are perpendicular to each other.

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