Momentum

  • In Newtonian physics momentum is the product of an object's mass, m and velocity, $ \vec v $ and consequently a vector quantity. Often given the symbol $ \vec P $, we can write the momentum of an object as:

    $ \vec P = m \vec v $

    In Newtonian physics, momentum is always conserved in a closed system. So if two objects collide, the momentum of the two bodies prior to the collision $  \vec P_{\rm i} $ (initial) is equal to their vector sum after the collision $ \vec P_{\rm f} $ (final). ie:

    $  \vec P_{\rm i} = m_1 \vec v_{\rm 1i} + m_2 \vec v_{\rm 2i} = m_1 \vec v_{\rm 1f} + m_2 \vec v_{\rm 2f} = \vec P_{\rm f} $

    At the microphysics level, even light has a momentum associated with it.

    In the physics of rotation, there is an analogue to momentum known as angular momentum, which is also conserved.

    Example: A 4 kg mass travelling at 2 ms-1 has the same momentum as a 1 kg mass travelling at 8 ms-1. If they were travelling in opposite directions and became bound after the collision, the resulting body would be stationary at the net momentum would be zero.
    Momentum example

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