Linear Momentum
Overview
For a particle, or body of some sort, the momentum is defined to be:
{% \vec{p} = m\vec{v} %}
When there is a collection of particles, indexed by {% i %}, the momentum of the system of particles is given by
{% \vec{P} = \sum_i m \vec{v}_i %}
Change of Momentum
In classical mechanics, the mass of body is a constant. Therefore, applying the
derivative of a product,
we get
{% \frac{d \vec{p}}{dt} = m \frac{d \vec{v}}{dt} %}
Then by Newtons second law, we get
{% \frac{d \vec{p}}{dt} = \vec{F} %}
That is, the rate of change of the momentum is simply the total force on the particle.
Conservation of Linear Momentum
Conservation of linear momentum follows simply from
Newtons third law.
That is, if particle {% i %} exerts a force {% F %} on particle {% j %},
then particle {% j %} exerts a force of {% -F %} on particle {% i %}.
