What is "moment of inertia"

Moment \Mo"ment\, n. [F. moment, L. momentum, for movimentum movement, motion, moment, fr. movere to move. See Move, and cf. Momentum, Movement.]

1. A minute portion of time; a point of time; an instant; as, at that very moment.

   In a moment, in the twinkling of an eye.
   --1 Cor. xv. 5

2. 2. Impulsive power; force; momentum.

   The moments or quantities of motion in bodies.
   --Berkley.

   Touch, with lightest moment of impulse, His free will.
   --Milton.

3. Importance, as in influence or effect; consequence; weight or value; consideration.

   Matters of great moment.
   --Shak.

   It is an abstruse speculation, but also of far less moment and consequence of us than the others.
   --Bentley.

4. An essential element; a deciding point, fact, or consideration; an essential or influential circumstance.

5. (Math.) An infinitesimal change in a varying quantity; an increment or decrement. [Obs.]

6. (Mech.) Tendency, or measure of tendency, to produce motion, esp. motion about a fixed point or axis. Moment of a couple (Mech.), the product of either of its forces into the perpendicular distance between them. Moment of a force. (Mech.)

   1. With respect to a point, the product of the intensity of the force into the perpendicular distance from the point to the line of direction of the force.

   2. With respect to a line, the product of that component of the force which is perpendicular to the plane passing through the line and the point of application of the force, into the shortest distance between the line and this point.

   3. With respect to a plane that is parallel to the force, the product of the force into the perpendicular distance of its point of application from the plane.

      Moment of inertia, of a rotating body, the sum of the mass of each particle of matter of the body into the square of its distance from the axis of rotation; -- called also moment of rotation and moment of the mass.

      Statical moment, the product of a force into its leverage; the same as moment of a force with respect to a point, line, etc.

      Virtual moment. See under Virtual.

      Syn: Instant; twinkling; consequence; weight; force; value; consideration; signification; avail.

n. 1 (context physics English) A measure of a body's resistance to a change in its angular rotation velocity 2 (context engineering English) A measure of a body's resistance to bending; second moment of inertia; second moment of area.

n. the tendency of a body to resist angular acceleration

The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body determines the torque needed for a desired angular acceleration about a rotational axis. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation. It is an extensive (additive) property: the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). One of its definitions is the second moment of mass with respect to distance from an axis r, $I = \int_{Q} r^2 \mathrm dm$, integrating over the entire mass Q.

For bodies constrained to rotate in a plane, it is sufficient to consider their moment of inertia about an axis perpendicular to the plane. For bodies free to rotate in three dimensions, their moments can be described by a symmetric 3 × 3 matrix; each body has a set of mutually perpendicular principal axes for which this matrix is diagonal and torques around the axes act independently of each other.