Force is derivative of momentum (vector)
========================================

Newton's second law of motion can be generalized in terms of linear momentum. Precisely,
the net force exerted on a body is equal to the time derivative of the body's momentum.

**Notes:**

#. Works in relativistic mechanics as well as in classical mechanics.

#. See :ref:`scalar counterpart <Force is derivative of momentum>` of this law.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Momentum#Relation_to_force>`__.

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

.. py:data:: time

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

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: momentum

    The magnitude of the :attr:`~symplyphysics.symbols.classical_mechanics.momentum` of the body as a function of :attr:`~time`.

Symbol:
    :code:`p(t)`

Latex:
    :math:`\mathbf{p} \left( t \right)`

Dimension:
    :code:`momentum`


.. py:data:: force

    The magnitude of the net :attr:`~symplyphysics.symbols.classical_mechanics.force` exerted on the body as a function of :attr:`~time`.

Symbol:
    :code:`F(t)`

Latex:
    :math:`\mathbf{F} \left( t \right)`

Dimension:
    :code:`force`


.. py:data:: force_law

    :code:`F(t) = Derivative(p(t), t)`


    Latex:
        .. math::
            \mathbf{F} \left( t \right) = \frac{d}{d t} \mathbf{p} \left( t \right)