#AP Physics C: Mechanics - Momentum Review 🚀

Hey! Let's get you totally prepped for the exam. We're diving into momentum, a core concept that ties into so much of what we've learned. Remember, momentum is all about how much 'oomph' an object has when it's moving. Let's break it down and make sure you're ready to rock this!

#Conservation of Linear Momentum

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• Think of a system of objects as a single entity with a collective center-of-mass velocity. It's like finding the average motion of the whole group. 🏃‍♂️
• Formula: $$\vec{v}_{\mathrm{cm}}=\frac{\sum \vec{p}_{i}}{\sum m_{i}}=\frac{\sum\left(m_{i} \vec{v}_{i}\right)}{\sum m_{i}}$$
• This velocity stays constant when no net external force acts on the system. It's like a group of friends moving together without anyone pushing them around from the outside.

#Sum of Momenta

• The total momentum of a system is simply the sum of all individual momenta. It's like adding up all the 'oomph' in the system.

#Changes in Momentum

• In an isolated system, momentum changes are always balanced. If one object gains momentum, another must lose an equal amount. It's a perfect give-and-take! 🤝
• This is directly related to Newton's third law: every action has an equal and opposite reaction. The impulse one object exerts on another is met with an equal and opposite reaction impulse.
• Key Idea: Choosing the right system boundaries is crucial. A smart choice can make the total momentum constant.
• Impulse-Momentum Theorem: Any change in a system's total momentum equals the impulse exerted on it from outside the system. It's like giving the system a push (impulse) which changes its motion (momentum).
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