Rotational inertia about axis and through center of mass
========================================================

The *parallel-axis theorem* relates the rotational inertia of a body about any axis to
that of the same body about a parallel axis that extends through the body's center of mass
of mass).

**Conditions:**

#. The two axes must be parallel to each other.
#. The axis used in the calculation of :math:`I_\text{com}` must pass through the body's center of mass.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Parallel_axis_theorem#Mass_moment_of_inertia>`__.

.. py:currentmodule:: symplyphysics.laws.kinematics.rotational_inertia.rotational_inertia_about_axis_and_through_center_of_mass

.. py:data:: rotational_inertia

    :attr:`~symplyphysics.symbols.classical_mechanics.rotational_inertia` about some axis.

Symbol:
    :code:`I`

Latex:
    :math:`I`

Dimension:
    :code:`length**2*mass`


.. py:data:: rotational_inertia_through_com

    :attr:`~symplyphysics.symbols.classical_mechanics.rotational_inertia` about an axis that is parallel to the given one and passes through
    the center of mass.

Symbol:
    :code:`I_com`

Latex:
    :math:`I_\text{com}`

Dimension:
    :code:`length**2*mass`


.. py:data:: mass

    The :attr:`~symplyphysics.symbols.basic.mass` of the body.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: distance_between_axes

    :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance` between the axes.

Symbol:
    :code:`d`

Latex:
    :math:`d`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`I = I_com + m * d^2`


    Latex:
        .. math::
            I = I_\text{com} + m d^{2}