Moment of inertia

The moment of inertia (also known as mass moment of inertia, angular/rotational mass, second moment of mass, or rotational inertia) is a measure of how difficult it is to change the rotation rate of a rigid body about a given axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis. It plays the same role in rotational motion as mass does in linear motion. A body's moment of inertia about a particular axis depends on both the mass and its distribution relative to the axis, increasing with mass and distance from the axis.

For a point mass, the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis.

If a body is forced to rotate in a plane, then only the moment of inertia about an axis perpendicular to the plane, a scalar value, matters. If a body is allowed to rotate in all three dimensions, then its moment is described by a symmetric three-by-three matrix. This symmetric matrix can be orthogonally diagonalized by a set of mutually perpendicular principal axes. Torques around these principal axes act independently of each other.