Centripetal acceleration via angular speed and radius
=====================================================

*Centripetal acceleration* is defined as the change in velocity tangential to the velocity vector.

**Links:**

#. `Physics LibreTexts, second part of equation 6.2.5 <https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/06%3A_Uniform_Circular_Motion_and_Gravitation/6.02%3A_Centripetal_Acceleration>`__.

.. py:currentmodule:: symplyphysics.laws.kinematics.centripetal_acceleration_via_angular_speed_and_radius

.. py:data:: centripetal_acceleration

    Centripetal, or normal, :attr:`~symplyphysics.symbols.classical_mechanics.acceleration`.

Symbol:
    :code:`a_n`

Latex:
    :math:`a_{n}`

Dimension:
    :code:`acceleration`


.. py:data:: angular_speed

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_speed`.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: radius_of_curvature

    Instantaneous :attr:`~symplyphysics.symbols.basic.radius_of_curvature`.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`a_n = w^2 * r`


    Latex:
        .. math::
            a_{n} = \omega^{2} r