#AP Physics C: Mechanics - Momentum and Impulse 🚀

Hey there, future AP Physics C champ! Let's dive into momentum and impulse – two concepts that are absolutely key to understanding how forces change motion. Think of this as your ultimate cheat sheet for acing the exam. Let's get started!

This topic is super important! Expect to see it in both multiple-choice and free-response questions. It's a core concept that links force, time, and motion. Understanding it well will boost your confidence and your score.

#Impulse Delivery 🏃‍♂️

#Rate of Momentum Change

• The net external force acting on a system dictates how quickly its momentum changes. 💡
• This is captured by the equation: $$\vec{F}_{\text {net }}=\frac{d \vec{p}}{d t}$$
  • $\vec{F}_{\text {net }}$ is the net external force vector.
  • $\frac{d \vec{p}}{d t}$ is the rate of change of momentum with respect to time.

#Impulse Definition

• Impulse is the effect of a force acting over a time interval. Think of it as a 'push' that changes momentum.
• Calculated using the integral: $$\vec{J}=\int_{t_{1}}^{t_{2}} \vec{F}_{\text {net }}(t) d t$$
  • $\vec{J}$ is the impulse vector.
  • $\vec{F}_{\text {net }}(t)$ is the net external force as a function of time.
  • $t_1$ and $t_2$ are the start and end times of the interval.

#Impulse Direction

• Impulse is a vector, meaning it has both magnitude and direction.
• It always points in the same direction as the net force applied.

#Impulse and Force-Time Graphs 📈

• The area under a force-time graph gives you the impulse delivered. It's a visual way to see the total 'push'.
• This area is the integral of the net force over time.