Moment of inertia

The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a <a href="/facts/Rigid_body/THezBlq2">rigid body</a> is defined relative to a rotational axis. It is the ratio between the <a href="/facts/Torque/KcrcvNtV">torque</a> applied and the resulting <a href="/facts/Angular_acceleration/jDv9uzAS">angular acceleration</a> about that axis.: 279 : 261  It plays the same role in rotational motion as <a href="/facts/Mass/HHdc8XmF">mass</a> does in linear motion. A body's moment of inertia about a particular axis depends both on the mass and its distribution relative to the axis, increasing with mass & distance from the axis.
It is an <a href="/facts/Intensive_and_extensive_properties/UcgSh8EG">extensive</a> (additive) property: for a <a href="/facts/Point_particle/4MPToN8W">point mass</a> the moment of inertia is simply the mass times the square of the <a href="/facts/Perpendicular_distance/P0aEswE4">perpendicular distance</a> 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 <a href="/facts/Moment_(physics)/WvgxtdhP">moment</a> of mass with respect to distance from an <a href="/facts/Axis_of_rotation/PGcg3IY5">axis</a>.
For bodies constrained to rotate in a plane, only their moment of inertia about an axis perpendicular to the plane, a <a href="/facts/Scalar_(physics)/05uvvP8N">scalar</a> value, matters. For bodies free to rotate in three dimensions, their moments can be described by a <a href="/facts/Symmetric_matrix/08CGwjNl">symmetric</a> 3-by-3 matrix, with a set of mutually perpendicular principal axes for which this matrix is <a href="/facts/Diagonal_matrix/tjIAHrE6">diagonal</a> and torques around the axes act independently of each other.
In <a href="/facts/Mechanical_engineering/cbId4fye">mechanical engineering</a>, simply "inertia" is often used to refer to "<a href="/facts/Inertial_Mass/KXtSKomS">inertial mass</a>" or "moment of inertia".

Moment of inertia open-in-new

Moment of inertia