# Using momentum in 2-D collisions, and the center of mass

In two dimensions, the total vector momentum is still conserved. That means that each component of momentum remains the same before and after the encounter.

• Hockey puck slides into brick
• Hockey puck slides into brick (again)

#### The center of mass: discrete case

When several objects collide or a single object explodes, the individual pieces may fly all over the place. However, if one considers all the pieces as a whole, via the total mass and motion of the center of mass, then Newton's Laws are simple and easy to solve again.

#### The center of mass: extended case

What about extended objects? Some of the nice rules you've learned so far in the class, such as

```

" ... in projectile motion, the x-velocity remains
constant while the y-velocity changes linearly with
time.  The trajectory of an object thus traces
a parabolic curve ...."

```

don't seem to work if you pick any arbitrary part of an extended body. For example, if I toss a baseball bat up into the air, a movie might show this: