SOLID STATE PRESS
← Back to catalog
Linear Momentum and Impulse cover
Coming soon
Coming soon to Amazon
This title is in our publishing queue.
Browse available titles
Physics

Linear Momentum and Impulse

A High School and Early College Physics Primer

Physics moving too fast? Momentum and impulse trip up more students than almost any other first-year topic — not because the ideas are hard, but because textbooks bury the core concepts under pages of derivation before you ever work a real problem.

**TLDR: Linear Momentum and Impulse** cuts straight to what you need. In roughly 15 focused pages, this primer covers momentum as a vector, the impulse-momentum theorem and why it explains everything from crumple zones to follow-through in sports, and the conservation law that makes collision problems solvable. You'll work through perfectly inelastic collisions, standard elastic cases, explosion problems, and a clean introduction to 2D collisions — all with signed numbers, worked examples, and the misconceptions called out before they catch you.

This guide is written for students taking high school physics or an introductory college mechanics course, and it's especially useful as a focused AP Physics 1 momentum impulse review in the days before an exam. It also works as a fast orientation for a parent or tutor who needs to get up to speed before a study session.

The book is short on purpose. Every sentence earns its place. There are no filler chapters, no padding, and no "in this section we will explore" throat-clearing — just the clearest path from confused to confident.

If a momentum or collision problem is standing between you and the grade you want, pick this up and read it today.

What you'll learn
  • Define linear momentum and impulse and use the correct units
  • Apply the impulse-momentum theorem to force-time problems
  • Use conservation of momentum to solve elastic and inelastic collisions in one dimension
  • Distinguish elastic, inelastic, and perfectly inelastic collisions using kinetic energy
  • Set up momentum conservation in two dimensions using component equations
  • Recognize and avoid common sign and reference-frame mistakes
What's inside
  1. 1. What Momentum Is and Why Physicists Care
    Introduces momentum as mass times velocity, explains why it is a vector, and motivates conservation as the deeper reason momentum matters.
  2. 2. Impulse and the Impulse-Momentum Theorem
    Defines impulse as force times time, derives the impulse-momentum theorem from Newton's second law, and works problems involving collisions, follow-through, and crumple zones.
  3. 3. Conservation of Momentum in One Dimension
    States the conservation principle, explains when it applies (no net external force on the system), and walks through sign conventions for 1D collision and explosion problems.
  4. 4. Elastic, Inelastic, and Perfectly Inelastic Collisions
    Classifies collisions by what happens to kinetic energy, derives the stick-together formula, and works the standard 1D elastic collision case.
  5. 5. Momentum in Two Dimensions
    Extends conservation to 2D by treating x and y components independently, with worked examples for billiard-ball and explosion problems.
  6. 6. Where This Shows Up: Rockets, Safety, and What Comes Next
    Connects momentum and impulse to rocket propulsion, vehicle safety design, and sports, and previews how the ideas extend to angular momentum and particle physics.
Published by Solid State Press
Linear Momentum and Impulse cover
TLDR STUDY GUIDES

Linear Momentum and Impulse

A High School and Early College Physics Primer
Solid State Press

Linear Momentum and Impulse

A High School and Early College Physics Primer

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Who This Book Is For

If you're a high school student looking for a focused momentum and impulse physics study guide, this book was written for you. It's also the right fit if you're doing AP Physics 1 momentum and impulse prep before exam season, or if you're a physics primer for first-year college students who showed up to class and found Newton's third law suddenly isn't enough anymore. Parents and tutors reviewing collision problems alongside a student will find it equally useful.

This short physics review book for exams covers the core ideas efficiently: what momentum is, how impulse changes it, and why conservation of momentum holds in closed systems. It works through elastic and inelastic collision explained simply — including perfectly inelastic cases — then extends everything to two dimensions. About 15 pages, no filler.

Read straight through in one sitting to build the conceptual spine, then work every worked example actively before moving to the conservation of momentum practice problems at the end. That's the whole method — this high school physics collisions review book does the rest.

Contents

  1. 1 What Momentum Is and Why Physicists Care
  2. 2 Impulse and the Impulse-Momentum Theorem
  3. 3 Conservation of Momentum in One Dimension
  4. 4 Elastic, Inelastic, and Perfectly Inelastic Collisions
  5. 5 Momentum in Two Dimensions
  6. 6 Where This Shows Up: Rockets, Safety, and What Comes Next
Chapter 1

What Momentum Is and Why Physicists Care

Pick up a bowling ball and a tennis ball and throw both as hard as you can. The bowling ball is obviously harder to stop — not just because it's heavier, but because all that mass is moving. Linear momentum captures exactly this idea: it is the product of an object's mass and its velocity.

$p = mv$

Here $p$ is momentum, $m$ is mass in kilograms, and $v$ is velocity in meters per second. The unit of momentum is therefore kg·m/s (kilogram-meters per second). There is no special named unit for momentum the way there is a Newton for force — you just carry the kg·m/s through your calculations.

Momentum is a vector

Because velocity is a vector — it has both a magnitude and a direction — momentum is also a vector quantity. This means a 2 kg ball moving right at 5 m/s and a 2 kg ball moving left at 5 m/s have momenta that are equal in size but opposite in sign. When you work problems in one dimension, you will pick a positive direction (usually rightward or upward) and assign negative values to anything moving the other way. Getting signs wrong is one of the most common mistakes in momentum problems, so establishing your positive direction before you write a single equation is a habit worth building now.

Example. A 0.15 kg baseball travels toward a batter at 40 m/s. Taking the direction toward the batter as negative, what is the ball's momentum?

Solution. $p = mv = (0.15\ \text{kg})(-40\ \text{m/s}) = -6\ \text{kg·m/s}$. The negative sign tells you the ball is moving toward the batter, not just that something went wrong.

Newton's second law, rewritten

You probably know Newton's second law as $F = ma$. There is a more general form that physicists actually use more often:

$F_{\text{net}} = \frac{\Delta p}{\Delta t}$

Keep reading

You've read the first half of Chapter 1. The complete book covers 6 chapters in roughly fifteen pages — readable in one sitting.

Coming soon to Amazon