A body's moment of inertia factor (short for polar moment of inertia factor, the one of interest), is a measure that characterizes the mass distribution within the body, of use in working out the dynamics of bodies' rotation, useful for objects such as stars, planets, and moons. It is independent of the object's mass and radius, and is a scalar within the range of 0 to 1. Example (polar) moment of inertia factor values:
|sphere of uniform density||0.4|
|object with higher density toward the surface||>0.4|
|object with higher density toward the center||<0.4|
A smaller number indicates more mass toward the center, i.e., a dense "core", and a body's higher total mass and lower rigidity contribute to this. The number is of interest regarding the rotation-history of the object, such as the timescale necessary for tidal forces to produce tidal locking.
An object's polar moment of inertia factor is:
The object's polar moment of inertia (moment of inertia around its axis of rotation) is a scalar characterizing the object's implied resistance around its axis of rotation. Such a moment of inertia of an object with respect to an axis is a measure of the ratio between a torque on the object with respect to that axis and the angular acceleration yielded by that torque:
C = L/ω or C = τ/α
For the axis of C:
The less-specific term, moment of inertia includes all the information to characterize an object's resistance to torque along any axis through its center of mass, i.e., the force it would take to change its rotation (much like the way mass determines what linear acceleration results from a given force). A single scalar is insufficient to hold all this information, which is generally represented as a 3×3 matrix, specifically a 3×3 tensor.