Impulse-Momentum Principle

The Principle of Linear Impulse and Momentum states that the initial linear momentum of an object plus the total linear impulse applied equals its final linear momentum.
$m{\mathbf{v}}_1+\sum {\int }_{t_1}^{t_2}\mathbf{F}dt=m{\mathbf{v}}_2$

For a constant net force ($\mathbf{F}$), the simplifies to:
$m{\mathbf{v}}_1+\sum \mathbf{F}\Delta t=m{\mathbf{v}}_2$

As seen above, the impulse due to weight force is considered negligible and isn’t factored into our equation.

Impulse and Momentum

Momentum is the product of an object’s mass and velocity:
$p=mv$

Impulse is the measure of how much a force changes an object’s momentum over a specific period of time.
$J={\int }_{t_1}^{t_2}Fdt$
If $F$ is constant, than impulse is simplified to:
$J=F\cdot \Delta t$

If there is no meaningful external impulses, then momentum is conserved.

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