Rotational inertia is additive
==============================

For a system composed of several parts, its total rotational inertia is the sum of the rotational
inertia of each part of the system.

**Conditions:**

#. The rotational inertia is calculated for the same axis for all parts of the system.

**Links:**

#. `Wikipedia, see second paragraph <https://en.wikipedia.org/wiki/Moment_of_inertia>`__.

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

.. py:data:: total_rotational_inertia

    Total :attr:`~symplyphysics.symbols.classical_mechanics.rotational_inertia` of the system.

Symbol:
    :code:`I`

Latex:
    :math:`I`

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


.. py:data:: index

    Index assigned to each part of the system.


.. py:data:: rotational_inertia

    :attr:`~symplyphysics.symbols.classical_mechanics.rotational_inertia` of the :math:`k`-th part of the system.

Symbol:
    :code:`I[k]`

Latex:
    :math:`{I}_{k}`

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


.. py:data:: law

    :code:`I = Sum(I[k], k)`


    Latex:
        .. math::
            I = \sum_k {I}_{k}