Torque is angular momentum derivative
=====================================

In the case of a single particle, the total vector sum of all the external torques acting on a
particle is equal to the time rate change of the angular momentum of that particle.

In the case of a system of particles, the net external torque acting on a system of particles is
equal to the time rate change of the system's total angular momentum.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Torque#Relationship_with_the_angular_momentum>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.vector.torque_is_angular_momentum_derivative

.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: angular_momentum

    Pseudovector of net :attr:`~symplyphysics.symbols.classical_mechanics.angular_momentum` as a function of :attr:`~time`.

Symbol:
    :code:`L(t)`

Latex:
    :math:`L \left( t \right)`

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


.. py:data:: torque

    Pseudovector of net :attr:`~symplyphysics.symbols.classical_mechanics.torque` as a function of :attr:`~time`.

Symbol:
    :code:`tau(t)`

Latex:
    :math:`\tau \left( t \right)`

Dimension:
    :code:`force*length`


.. py:data:: law

    :code:`tau(t) = Derivative(L(t), t)`


    Latex:
        .. math::
            \tau \left( t \right) = \frac{d}{d t} L \left( t \right)