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 :doc:`laws.kinematics.vector.centrifugal_acceleration_via_centripetal_acceleration`.

**Notation:**

#. :math:`\vec a \times \vec b` (:code:`cross(a, b)`) is the cross product between :math:`\vec a` and :math:`\vec b`.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Centripetal_force#Derivation_using_vectors>`__.

.. py:currentmodule:: symplyphysics.laws.kinematics.vector.centripetal_acceleration_via_cross_product



.. py:function:: centripetal_acceleration_law(angular_velocity_, radius_vector_)

    Centripetal acceleration via angular velocity and radius vector.

    Law:
        :code:`a_c = cross(w, cross(w, r))`

    Latex:
        .. math::
            {\vec a}_\text{c} = \vec \omega \times (\vec \omega \times \vec r)

    :param angular_velocity\_: pseudovector of angular velocity

        Symbol: :code:`w`

        Latex: :math:`\vec \omega`

        Dimension: *angle* / *time*

    :param radius_vector\_: radius vector, or position vector

        Symbol: :code:`r`

        Latex: :math:`\vec r`

        Dimension: *length*

    :return: vector of centripetal acceleration

        Symbol: :code:`a_c`

        Latex: :math:`{\vec a}_\text{c}`

        Dimension: *acceleration*