>[!summary] Linear momentum describes how much force effects motion Impulse is the change in linear momentum over time > Linear momentum is a intrinsic property > **Key equations:** $p = mv$ $I = F\Delta t$ >[!info]+ Read Time **⏱ 2 mins** # General Principle Linear momentum is a conserved quantity and describes how much force effects motion and is a intrinsic property >[!info] Important High momentum - Harder to stop Low momentum - easier to stop >[!warning] Assumptions If we assume mass is constant and newtons second law ([[Dynamic Forces & Newtons Laws#Newtons Laws]]) is true. $\begin{array}{c} \frac{dp}{dt} = \frac{d}{dt}(mv) \\ F = \frac{dp}{dt} = ma \\ p = mv \end{array}$ # Impulse Impulse is the change in momentum over time. If we assume mass is the same like in linear momentum, we can derive a principle for impulse. $\begin{array}{c} F = \frac{dp}{dt}\\ I = \int_{t_i} ^ {t_f} F(t)dt \\ \text{If F is consant the equation becomes} \\ I = F\Delta t \end{array}$ ![[lin_1.png]] [^1] >[!note] Explanation Impulse is the area inside F and t graph >[!bug] Difference between Impulse and work A **force** acting over **displacement** transfer **energy** - **Work** A **force** acting over **time** transfers **momentum** - **Impulse** [^1]: Taken from R. Epp Lecture notes. --- > 💡 Found this concept helpful? [Star Math & Matter on GitHub](https://github.com/rajeevphysics/Obsidan-MathMatter) to support more intuitive science breakdowns like this. ---