Impulse-Momentum Theorem

Summary

The Impulse momentum theorem relates impulse and momentum

Key Equation:

Impulse-Momentum theorem:
$I = Δ p$

Read Time

⏱ 1 min

Definition

The impulse momentum theorem is a theorem that relates impulse and linear momentum.

Assumptions

To relate impulse and momentum, assume the following:

Impulse is defined as $I = \int_{t_{1}}^{t_{2}} F (t) d t$
The instantaneous change on momentum can be described by newtons second law $F = \frac{d p}{d t}$

\begin{matrix} \begin{aligned} \int_{t_{1}}^{t_{2}} F (t) d t & = \int_{t_{1}}^{t_{2}} \frac{d p}{d t} d t \\ = \int_{t_{1}}^{t_{2}} d p \\ = p (t_{2}) - p (t_{1}) \\ = Δ p \end{aligned} \\ Therefore: \\ I = Δ p \end{matrix}