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:`\left( \vec a, \vec b \right)` (:code:`dot(a, b)`) is the dot product between
   vectors :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_vector_rejection

.. py:data:: centripetal_acceleration

    Vector of the body's centripetal :attr:`~symplyphysics.symbols.classical_mechanics.acceleration`.

Symbol:
    :code:`a_cp`

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

Dimension:
    :code:`acceleration`


.. py:data:: angular_velocity

    Pseudovector of the angular velocity of the body's rotation. See :attr:`~symplyphysics.symbols.classical_mechanics.angular_speed`.

Symbol:
    :code:`w`

Latex:
    :math:`{\vec \omega}`

Dimension:
    :code:`angle/time`


.. py:data:: position_vector

    The body's position vector. See :attr:`~symplyphysics.symbols.classical_mechanics.distance_to_origin`.

Symbol:
    :code:`r`

Latex:
    :math:`{\vec r}`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`a_cp = w * dot(r, w) - r * dot(w, w)`


    Latex:
        .. math::
            {\vec a}_\text{cp} = {\vec \omega} \left( {\vec r}, {\vec \omega} \right) - {\vec r} \left( {\vec \omega}, {\vec \omega} \right)