Momentum and Impulse

Definition: Linear momentum

$$\vec{p} \vec{v}$$ (1)

Note:

• Momentum is a vector.
• The units of linear momentum are: kg m/s.

We can rewrite Newton's Second Law in terms of momentum:

$$\Sigma \vec{F} \vec{a} {\frac{\Delta v}{\Delta t}} {\frac{\Delta p}{\Delta t}}$$ (2)

Interpretation: Force can be expressed as:

$${\frac{\hbox{the change in momentum}}{\hbox{the time to make the change}}}$$

Definition: Impulse ( $\vec{I}$ )

$$\vec{I} \vec{F} \Delta \Delta \vec{p}$$ (3)

Note: Usually the force is a strongly dependent function of time. In this case, we need to use the average force in the above equation.