Moment of inertia

Moment of inertia measures how strongly an object resists angular acceleration about a specified axis. It depends on both the object's mass and how that mass is distributed around the axis.

Parallel axis theorem: A theorem relating moments of inertia about parallel axes through an object's center of mass and elsewhere. It calculates the moment of inertia when the rotation axis is shifted from the center of mass.
Mass: A measure of an object's inertia and its response to forces. Mass supplies the quantities that are distributed and weighted in moment-of-inertia calculations.
Flywheel: A rotating mechanical device that stores energy through its rotational motion. A large moment of inertia helps a flywheel store energy and resist speed changes.
Second moment of area: A geometric property of a cross-section that measures its distribution around an in-plane axis. It resembles a moment of inertia mathematically but contains area, not mass.
Perpendicular axis theorem: For a planar lamina, the moment of inertia about a perpendicular axis equals the sum for two perpendicular axes in its plane. It derives a perpendicular-axis value from two in-plane values for flat objects.
Rigid body: An idealized object whose internal distances remain fixed during motion. Rigid-body assumptions allow its mass distribution to be treated as fixed during rotation.
Bicycle wheel: A wheel used to propel or support a bicycle, with mass distributed around its rim, spokes, and hub. Its mass distribution affects the torque needed to change its spin.
Polar moment of area: A geometric property of a cross-section measuring area distribution around an axis perpendicular to its plane. It is used in torsion calculations and is distinct from mass moment of inertia.
Radius of gyration: The distance from an axis at which an object's entire mass could be concentrated without changing its moment of inertia. It expresses the mass distribution as an equivalent single distance from the axis.
Rotation axis: A line about which an object rotates or its rotational motion is described. The moment of inertia is defined relative to this chosen line.

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