Definition:Axial Vector

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Definition

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 $\mathbf V$.


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:


Right-hand-screw-rule.png


Also known as

An axial vector is also known as a pseudovector.


Examples

Angular Velocity

Angular velocity is an axial vector.


Angular Acceleration

Angular acceleration is an axial vector.


Also see


Sources