Period of torsion pendulum from rotational inertia
==================================================

A torsion pendulum is an angular version of a linear harmonic oscillator: a disk
oscillates in a horizontal plane; the reference line oscillates with some angular amplitude.
The element of elasticity is associated with the twisting of the suspension wire.

**Links:**

#. `Wikipedia, third formula <https://en.wikipedia.org/wiki/Torsion_spring#Torsional_harmonic_oscillators>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.period_of_torsion_pendulum_from_rotational_inertia

.. py:data:: period

    The :attr:`~symplyphysics.symbols.basic.period` of pendulum's oscillations.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`time`


.. py:data:: rotational_inertia

    The :attr:`~symplyphysics.symbols.classical_mechanics.rotational_inertia` of the disk.

Symbol:
    :code:`I`

Latex:
    :math:`I`

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


.. py:data:: torsion_stiffness

    The :attr:`~symplyphysics.symbols.classical_mechanics.torsion_stiffness`, which depends on the properties of the suspension wire.

Symbol:
    :code:`kappa`

Latex:
    :math:`\kappa`

Dimension:
    :code:`force*length/angle`


.. py:data:: law

    :code:`T = 2 * pi * sqrt(I / kappa)`


    Latex:
        .. math::
            T = 2 \pi \sqrt{\frac{I}{\kappa}}