Now that we have learned about energy we might wonder if there are other quantities that are conserved. The answer is yes there are, in fact much of physics involves trying to find these conserved quantities. The next one we will discuss is called momentum.  Momentum is the product of mass and velocity.  It is generally given the symbol p, which doesn’t make much sense, but the term used for momentum back in Newton’s time is impetus, which is where the p comes from.  So we have

\vec{p} = m \vec{v}

The French philosopher Descartes is often credited with the idea of momentum, though he didn’t use equation to describe it.  Newton new about momentum, in fact Newton’s second law can be expressed in terms of momentum.

\Sigma \vec{F} = {d\vec{p}\over{dt}}

If mass is constant then this derivative just gives ma.  But defining the net force in terms of the change of momentum also includes the possibility that the mass could change too. If we integrate the net force over time we then get the change in momentum which is called impulse.

\Delta p = \int_{t_1}^{t_2} F(t) dt

From Newton’s laws we can see that momentum should be conserved if two objects interact with one another like in a collision.