Axis of rotation

An axis of rotation is a line about which a body turns. For a rigid body rotating around a fixed axis, points on the axis remain stationary while other points trace circles.

Angular velocity: Angular velocity measures the rate and direction of rotation. Its direction lies along the rotation axis, while its magnitude gives the turning rate.
Rotation matrix: A rotation matrix is a linear transformation that rotates vectors while preserving lengths and angles. Its entries can encode a rotation around a specified axis.
Gyroscope: A gyroscope is a device that uses angular momentum to measure or maintain orientation. Its spinning rotor's axis helps define and track orientation.
Instantaneous axis of rotation: The instantaneous axis of rotation is the line about which a body's motion can be represented as rotation at a given instant. Unlike a fixed axis, it can change position or direction throughout a motion.
Moment of inertia: Moment of inertia measures how strongly a body's mass distribution resists angular acceleration about an axis. Changing the axis can change this rotational measure even when the body stays the same.
Cross product: The cross product of two vectors is a vector perpendicular to both, with direction set by the right-hand rule. It expresses the perpendicular direction used to represent angular velocity and torque.
Earth's rotation: Earth's rotation is its daily spin about an axis passing near the geographic poles. Earth provides a familiar example of a body's rotation axis.
Euler angles: Euler angles describe orientation through three successive rotations about specified axes. They represent changing three-dimensional orientation without requiring one permanent rotation axis.
Rigid body: A rigid body is an idealized object whose internal distances remain constant during motion. A fixed axis gives a simple description of a rigid body's rotation.
Coordinate system: A coordinate system assigns numbers to locations using a chosen origin, axes, and units. Describing an axis requires specifying its position and direction relative to coordinates.

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