Centripetal acceleration via vector rejection
=============================================

*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.centripetal_acceleration_via_cross_product`.

**Notation:**

#. :math:`|\vec a|` (:code:`norm(a)`) is the Euclidean norm of :math:`\vec a`.
#. :math:`\text{oproj}_{\vec b} \vec a` (:code:`reject(a, b)`) is the rejection of
   :math:`\vec a` from :math:`\vec b`, i.e. the component of :math:`\vec a` orthogonal
   to :math:`\vec b`.

**Links:**

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

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



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

    Centripetal acceleration via angular velocity and radius vector.

    Law:
        :code:`a_c = -1 * norm(w)^2 * reject(r, w)`

    Latex:
        .. math::
            {\vec a}_\text{c} = - |\vec \omega|^2 \text{oproj}_{\vec \omega} \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*