Perfectly inelastic collisions show up on nearly every high school physics test and AP Physics exam — and they trip students up every time. Objects stick together, momentum is conserved, kinetic energy mysteriously disappears, and then there's a 2D version where you have to split everything into components. If any of that sounds like a wall you've been staring at, this guide is for you.

**TLDR: Perfectly Inelastic Collisions** covers exactly what you need and nothing you don't. You'll learn what separates perfectly inelastic collisions from elastic and inelastic ones, how to set up and solve momentum conservation problems in one dimension with the right sign conventions, and why kinetic energy is not conserved — and how to calculate exactly how much is lost. The guide then extends the method to two-dimensional momentum problems by working through x- and y-components independently, and closes with the three classic setups that appear again and again: the ballistic pendulum, train-car coupling, and car crash problems.

This guide is written for high school students in grades 9–12 and early college students who need a fast, clear orientation to the topic — not a 400-page textbook. Every key term is defined in plain language, every equation is explained in words alongside the math, and every concept is grounded in worked, numbered examples.

If you've been searching for AP physics collision types explained simply, or just need a reliable resource before tomorrow's test, pick this up and get to work.

• Define a perfectly inelastic collision and distinguish it from elastic and general inelastic collisions.
• Apply conservation of momentum to find the final velocity when two objects stick together.
• Calculate the kinetic energy lost in a perfectly inelastic collision and explain where that energy goes.
• Solve two-dimensional perfectly inelastic collision problems using vector components.
• Recognize perfectly inelastic collisions in real-world contexts like car crashes, ballistic pendulums, and coupling train cars.

1. 1. What Makes a Collision 'Perfectly Inelastic'
   Defines the three categories of collisions and isolates what makes a collision perfectly inelastic: the objects stick together and move with one common velocity.
2. 2. Conservation of Momentum: The Master Equation
   Derives and applies the one-dimensional momentum conservation equation for perfectly inelastic collisions, with sign conventions and worked examples.
3. 3. Where Did the Energy Go? Kinetic Energy Loss
   Shows how to compute kinetic energy before and after the collision, why KE is not conserved, and what fraction is lost in typical setups.
4. 4. Two-Dimensional Collisions: Working with Components
   Extends momentum conservation to 2D by treating x- and y-components independently, with a worked intersection-collision example.
5. 5. Classic Problems and Real-World Applications
   Walks through the ballistic pendulum, train-car coupling, and car crash problems, showing how perfectly inelastic collisions appear in physics class and real life.