Kinetic energy via angular momentum and angular velocity
========================================================

Kinetic energy of a body rotating around a fixed or instantaneous axis depends on its
angular momentum and angular velocity.

.. py:currentmodule:: symplyphysics.laws.dynamics.vector.kinetic_energy_via_angular_momentum_and_angular_velocity



.. py:function:: kinetic_energy_law(angular_momentum_, angular_velocity_)

    Kinetic energy of a rotating body.

    **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`.

    Law:
        :code:`K = 1/2 * dot(L, w)`

    Latex:
        :math:`K = \frac{1}{2} \left(\vec L, \vec \omega \right)`

    :param angular_momentum\_: angular momentum of the body.

        Symbol: :code:`L`

        Latex: :math:`\vec L`

        Dimension: *length* * *momentum*

    :param angular_velocity\_: angular velocity of the body.

        Symbol: :code:`w`

        Latex: :math:`\vec \omega`

        Dimension: *angle* / *time*

    :return: kinetic energy of the body

        Symbol: :code:`K`

        Dimension: *energy*