Definition:Axial Vector

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Definition 1

An axial vector is a vector quantity $\mathbf V$ used to specify action which takes place around an axis of rotation.

In this case, the $\mathbf V$ is considered as acting parallel to the axis about which $\mathbf V$ acts.

As for a polar vector, the length of $\mathbf V$ indicates the magnitude of $\mathbf V$.

Definition 2

An axial vector is a vector quantity $\mathbf V$ which is not transformed to its negative when you reverse the axes of the coordinate system in which $\mathbf V$ is embedded.

The direction of $\mathbf V$ is determined by convention to be according to the right-hand rule.

Right-Hand Rule

Let $\mathbf V$ be an axial vector acting with respect to an axis of rotation $R$.

Consider a right hand with its fingers curled round $R$ so that the fingers are pointed in the direction of rotation of $\mathbf V$ around $R$.

The right-hand rule is the convention that the direction of $\mathbf V$ is the direction in which the thumb is pointing:


Also known as

An axial vector is also known as a pseudovector.



Rotation is an axial vector.

Angular Velocity

Angular velocity is an axial vector.

Angular Acceleration

Angular acceleration is an axial vector.

Also see

  • Results about axial vectors can be found here.