Angular position via constant angular acceleration and time
===========================================================

If a body is rotating with a constant acceleration, its angular position is a quadratic function of time.

#. The axis is fixed.
#. Angular acceleration is constant, i.e. :math:`\frac{d \alpha}{d t} = 0.`

**Links:**

#. `Wikipedia, second out of the last four equations in the paragraph <https://en.wikipedia.org/wiki/Kinematics#Acceleration_2>`__.

.. py:currentmodule:: symplyphysics.laws.kinematics.angular_position_via_constant_angular_acceleration_and_time

.. py:data:: final_angular_position

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_distance` at :attr:`~time`.

Symbol:
    :code:`theta`

Latex:
    :math:`\theta`

Dimension:
    :code:`angle`


.. py:data:: initial_angular_position

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_distance` at :math:`t = 0`.

Symbol:
    :code:`theta_0`

Latex:
    :math:`\theta_{0}`

Dimension:
    :code:`angle`


.. py:data:: initial_angular_speed

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_speed` at :math:`t = 0`.

Symbol:
    :code:`w_0`

Latex:
    :math:`\omega_{0}`

Dimension:
    :code:`angle/time`


.. py:data:: angular_acceleration

    Constant :attr:`~symplyphysics.symbols.classical_mechanics.angular_acceleration`.

Symbol:
    :code:`alpha`

Latex:
    :math:`\alpha`

Dimension:
    :code:`angle/time**2`


.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time` at which :attr:`~final_angular_position` is measured.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: law

    :code:`theta = theta_0 + w_0 * t + alpha * t^2 / 2`


    Latex:
        .. math::
            \theta = \theta_{0} + \omega_{0} t + \frac{\alpha t^{2}}{2}