> [!summary] The Impulse momentum theorem relates impulse and momentum > **Key Equation:** > Impulse-Momentum theorem: $I = \Delta p$ >[!info]+ Read Time **⏱ 1 min** # Definition The impulse momentum theorem is a theorem that relates [[Impulse|impulse]] and [[Linear Momentum|linear momentum]]. ## Derivation > [!warning] Assumptions To relate impulse and momentum, assume the following: > - [[Impulse|Impulse]] is defined as $I = \int_{t_{1}}^{t_{2}}F (t) dt$ > - The [[Instantaneous|instantaneous change]] on [[Linear Momentum|momentum]] can be described by [[Newton Laws|newtons second law]] $F = \frac{dp}{dt}$ $ \begin{array}{c} \\ \\ \begin{align*} \int_{t_{1}}^{t_{2}} F(t)dt &=\int_{t_{1}}^{t_{2}} \frac{dp}{dt}dt \\ &= \int_{t_{1}}^{t_{2}} dp \\ &= p(t_{2})-p(t_{1}) \\ &= \Delta p \end{align*} \\ \\ \text{Therefore:} \\ I = \Delta p \end{array} $ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/E13h1E_Pc00?si=icbo6hgh2X6oJt6Z" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>