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 :ref:`Centrifugal acceleration via centripetal acceleration`.

**Notation:**

#. :math:`\left[ \vec a, \vec b \right]` (: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.classical_mechanics.kinematics.rotational_motion.centripetal_acceleration_via_cross_product

.. py:data:: centripetal_acceleration

    Vector of 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 angular velocity of the body. See :attr:`~symplyphysics.symbols.classical_mechanics.angular_speed`.

Symbol:
    :code:`w`

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

Dimension:
    :code:`angle/time`


.. py:data:: position_vector

    Position vector of the body. 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 = cross(w, cross(w, r))`


    Latex:
        .. math::
            {\vec a}_\text{cp} = \left[ {\vec \omega}, \left[ {\vec \omega}, {\vec r} \right] \right]