Sphere rotating around one of its diameters
The angular velocity of the particle at P with respect to the origin O is determined by the perpendicular component of the velocity vector v.
An example of rotation. Each part of the worm drive—both the worm and the worm gear—is rotating on its own axis.
The orbital angular velocity vector encodes the time rate of change of angular position, as well as the instantaneous plane of angular displacement. In this case (counter-clockwise circular motion) the vector points up.
Schematic construction for addition of angular velocity vectors for rotating frames
Diagram showing Euler frame in green
Position of point P located in the rigid body (shown in blue). Ri is the position with respect to the lab frame, centered at O and ri is the position with respect to the rigid body frame, centered at . The origin of the rigid body frame is at vector position R from the lab frame.
Proving the independence of spin angular velocity from choice of origin

Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin.

- Angular velocity

The angular velocity vector also points along the axis of rotation in the same way as the angular displacements it causes.

- Rotation around a fixed axis
Sphere rotating around one of its diameters

3 related topics with Alpha

Overall

A sphere rotating (spinning) about an axis

Rotation

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A sphere rotating (spinning) about an axis
Rotation (angular displacement) of a planar figure around a point
Rotational Orbit v Spin
Relations between rotation axis, plane of orbit and axial tilt (for Earth).
Star trails caused by the Earth's rotation during the camera's long exposure time.
Euler rotations of the Earth. Intrinsic (green), Precession (blue) and Nutation (red)
The principal axes of rotation in space

Rotation is the circular movement of an object around an axis of rotation in either the clockwise or counterclockwise direction.

The angular velocity vector (an axial vector) also describes the direction of the axis of rotation.

Finding the direction of the cross product by the right-hand rule

Right-hand rule

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Common mnemonic for understanding orientation of axes in three-dimensional space.

Common mnemonic for understanding orientation of axes in three-dimensional space.

Finding the direction of the cross product by the right-hand rule
Conventional direction of the axis of a rotating body
Left-handed coordinates on the left, right-handed coordinates on the right.
Left- and right-handed screws
Prediction of direction of field (B), given that the current I flows in the direction of the thumb
Finding direction of magnetic field (B) for an electrical coil
Illustration of the right-hand rule on the ninth series of the Swiss 200-francs banknote.

In mathematics, a rotating body is commonly represented by a pseudovector along the axis of rotation.

The length of the vector gives the speed of rotation and the direction of the axis gives the direction of rotation according to the right-hand rule: right fingers curled in the direction of rotation and the right thumb pointing in the positive direction of the axis.

The position of a rigid body is determined by the position of its center of mass and by its attitude (at least six parameters in total).

Rigid body

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Solid body in which deformation is zero or so small it can be neglected.

Solid body in which deformation is zero or so small it can be neglected.

The position of a rigid body is determined by the position of its center of mass and by its attitude (at least six parameters in total).

Velocity (also called linear velocity) and angular velocity are measured with respect to a frame of reference.

Two points of a rotating body will have the same instantaneous velocity only if they happen to lie on an axis parallel to the instantaneous axis of rotation.