Linear displacement is angular displacement cross radius
========================================================

Assuming a body rotating around a fixed axis, the vector of its linear displacement can be expressed
as the cross product of the pseudovector of angular displacement and the radius vector of rotation.

**Conditions:**

#. The axis is fixed.
#. Angular displacement pseudovector and radius vector must be orthogonal to one another.

**Links:**

#. `Physics LibreTexts, formula 11.1.4 <https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/11%3A_Rotational_dynamics/11.01%3A_Rotational_kinematic_vectors>`__.

.. py:currentmodule:: symplyphysics.classical_mechanics.kinematics.rotational_motion.displacement_is_angular_displacement_cross_radius

.. py:data:: linear_displacement

    Vector of the body's linear displacement. See :attr:`~symplyphysics.symbols.classical_mechanics.distance`.

Symbol:
    :code:`s`

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

Dimension:
    :code:`length`


.. py:data:: angular_displacement

    Pseudovector of the body's angular displacement. See :attr:`~symplyphysics.symbols.classical_mechanics.angular_distance`. It is parallel
    to the rotation axis.

Symbol:
    :code:`theta`

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

Dimension:
    :code:`angle`


.. py:data:: rotation_radius_vector

    Radius vector pointing away from the rotation axis perpendicular to it. See
    :attr:`~symplyphysics.symbols.classical_mechanics.distance_to_axis`.

Symbol:
    :code:`r`

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

Dimension:
    :code:`length`


.. py:data:: law

    :code:`s = cross(theta, r)`


    Latex:
        .. math::
            {\vec s} = \left[ {\vec \theta}, {\vec r} \right]