Acceleration is normal plus tangential acceleration
===================================================

The acceleration of a body moving arbitrarily is composed of two parts:

#. *normal, or centripetal, acceleration*, which is always present in a rotating environment
   and points to the instantaneous axis of rotation,
#. and *tangential acceleration*, which is responsible for the change in the magnitude of
   the velocity vector.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Circular_motion#Formula>`__.

#. `Mathematica LibreTexts <https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/2%3A_Vector-Valued_Functions_and_Motion_in_Space/2.6%3A_Tangential_and_Normal_Components_of_Acceleration>`__.

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



.. py:function:: acceleration_law(normal_acceleration_, tangential_acceleration_)

    Total acceleration via normal and tangential accelerations.

    Law:
        :code:`a = a_n + a_t`

    Latex:
        .. math::
            \vec a = {\vec a}_n + {\vec a}_\tau

    :param normal_acceleration\_: vector of normal acceleration

        Symbol: :code:`a_n`

        Latex: :math:`{\vec a}_n`

        Dimension: *acceleration*

    :param tangential_acceleration\_: vector of tangential acceleration

        Symbol: :code:`a_t`

        Latex: :math:`{\vec a}_\tau`

        Dimension: *acceleration*

    :return: vector of total acceleration

        Symbol: :code:`a`

        Latex: :math:`\vec a`

        Dimension: *acceleration*


.. py:function:: normal_acceleration_law(total_acceleration_, tangential_acceleration_)

    Normal acceleration via total and tangential accelerations.

    Law:
        :code:`a_n = a - a_t`

    Latex:
        .. math::
            {\vec a}_n = \vec a - {\vec a}_\tau

    :param total_acceleration\_: vector of total acceleration

        Symbol: :code:`a`

        Latex: :math:`\vec a`

        Dimension: *acceleration*

    :param tangential_acceleration\_: vector of tangential acceleration

        Symbol: :code:`a_t`

        Latex: :math:`{\vec a}_\tau`

        Dimension: *acceleration*


.. py:function:: tangential_acceleration_law(total_acceleration_, normal_acceleration_)

    Tangential acceleration via total and normal accelerations.

    Law:
        :code:`a_t = a - a_n`

    Latex:
        .. math::
            {\vec a}_\tau = \vec a - {\vec a}_n

    :param total_acceleration\_: vector of total acceleration

        Symbol: :code:`a`

        Latex: :math:`\vec a`

        Dimension: *acceleration*

    :param normal_acceleration\_: vector of normal acceleration

        Symbol: :code:`a_n`

        Latex: :math:`{\vec a}_n`

        Dimension: *acceleration*