Centripetal acceleration via cross product

Centripetal acceleration is the acceleration of a body in a rotating coordinate system which is directed towards the axis of rotation.

Also see Centrifugal acceleration via centripetal acceleration.

Notation:

  1. \(\vec a \times \vec b\) (cross(a, b)) is the cross product between \(\vec a\) and \(\vec b\).

Links:

  1. Wikipedia.

centripetal_acceleration_law(angular_velocity_, radius_vector_)[source]

Centripetal acceleration via angular velocity and radius vector.

Law:

a_c = cross(w, cross(w, r))

Latex:
\[{\vec a}_\text{c} = \vec \omega \times (\vec \omega \times \vec r)\]
Parameters:

  • angular_velocity_ –

    pseudovector of angular velocity

    Symbol: w

    Latex: \(\vec \omega\)

    Dimension: angle / time

  • radius_vector_ –

    radius vector, or position vector

    Symbol: r

    Latex: \(\vec r\)

    Dimension: length

Returns:

vector of centripetal acceleration

Symbol: a_c

Latex: \({\vec a}_\text{c}\)

Dimension: acceleration