Newton originally wrote his Second Law in a different form, a form that is actually more general than the one we've been using.

ΣF

=

ma

=

m

dv dt

=

d(mv) dt

We can get away with writing the above equation under what condition?

That equation is true as long as mass is constant - so far we have only looked at constant-mass situtions, so ΣF = ma was fine. A good example of a system where the mass changes is a rocket - a rocket changes velocity by throwing mass away from itself at high speed. Now mass and velocity change, so we need a slightly more sophisticated force equation.

Our equation above also has the quantity mv in it - a net force on an object produces a change in this quantity.

Can you think of a good name for this quantity, mv, that is so directly tied to the net force?

We call mv momentum, and give it the symbol p.

General form of Newton's Second Law:

ΣF

=

dp dt

=

d(mv) dt

Apply the chain rule to the expression above:

General form of Newton's Second Law:

ΣF

= m

dv dt

+ v

dm dt

This reduces to ΣF = ma if the mass is constant.

Turning the general equation around, expressing it as an integral, we get:

∫ F dt = Δp

A net force acting over a time interval is called an impulse.
Impulse is the product of the force and the time interval over which the net force acts.
An impulse produces a change in momentum.
The impulse is the area under the net force vs. time graph.