Tangential acceleration via angular acceleration and radius
===========================================================

The tangential acceleration of a rotating body represents the change in magnitude
of the velocity vector, and its vector is tangent to the path of the body.

**Conditions:**

#. Radius is constant, i.e. :math:`\frac{d r}{d t} = 0.`

**Links:**

#. Equation 10-22 on p. 269 of "Fundamentals of Physics" by David Halladay et al., 10th Ed.

.. py:currentmodule:: symplyphysics.laws.kinematics.tangential_acceleration_via_angular_acceleration_and_radius

.. py:data:: tangential_acceleration

    Tangential :attr:`~symplyphysics.symbols.classical_mechanics.acceleration`.

Symbol:
    :code:`a_t`

Latex:
    :math:`a_{\tau}`

Dimension:
    :code:`acceleration`


.. py:data:: angular_acceleration

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

Symbol:
    :code:`alpha`

Latex:
    :math:`\alpha`

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


.. py:data:: radius_of_curvature

    Instantaneous :attr:`~symplyphysics.symbols.basic.radius_of_curvature`.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`a_t = alpha * r`


    Latex:
        .. math::
            a_{\tau} = \alpha r