(5)+Systems+of+Particles+and+Momentum

PAGE EDITOR(S): Julian "Lonestar" HK, Andrew "The Hash Slinging Slasher" Roberts, Zack "The Bargain Hunter" Berman

OK, so our topics are Systems of Particles (aka Centers of Mass, henceforth known as COMs) and Momentum (henceforth known as momentum).

__Center of Mass__ Let's start with COMs. It's pretty easy. All you have to know (or almost all you have to know) is:

1. You are given an object and its mass or a system and the masses of the objects within it. 2. Split the object (or system) into easily measurable pieces and establish coordinates for the COM's of each piece. 3. Plug the coordinates and the mass of each piece into:

4. High-five your buddies cause you're sour cream and done-ions.

Guess what else! If you know the dimensions of the object and the object has uniform mass distribution, you can find the center of mass without knowing the actual mass of the object. Simply replace the masses in the center of mass equation with the areas (or volume) of each individual part of the object. Because area (or volume) is proportional to mass in this case, the answer will be the same.

But wait! There's more! The equations for velocity and acceleration are very similar:



With no external forces, there will be no acceleration of the center of mass and the velocity will remain constant. Cool, huh?

__Momentum__ Momentum is similarly very easy. The basic formula you need to evaluate is: The catch that keeps this from being the simplest type of problem is that you need to first figure out what type of collision you are watching/experiencing. The three types of collisions are:

1. **Elastic/Perfectly Elastic** - in this type of collision, Kinetic Energy is conserved. You will solve these problems using both the formula for momentum and Examples include collision cart experiments, ideal gas experiments, and magnets.

2. **Inelastic -** kinetic energy is **NOT** conserved. It's lost through light, sound, heat, etc. The objects will collide and then **separate**. Examples include car crashes and basically almost every collision in the real world.



3. **Perfectly/Totally/Completely Inelastic -** Kinetic energy is not conserved in this type of collision. However, the objects will collide and then **stick together.** Examples include shooting a bullet at a block or catching a ball. You will solve these problems using momentum equations where it is

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