Momentum, which is given the symbol p , is a combination of the mass and velocity of something that is moving. Mathematically, momentum is described by the equation:

In this equation, the p and v are in bold because momentum and velocity are considered vector quantities. That means that they have both a magnitude and direction.

Understanding momentum can lead to some surprising answers to questions. For example, consider the question "If a BB bumped into a bowling ball, would the bowling ball move?" The answer to the question depends upon how much momentum the bb has. If the bb was not going very fast it would not have much momentum and the bowling ball would not move very much (you probably could not even measure any motion in most cases). If the BB was going very fast, though, it would be a different story. If a bb that weighed 57 grams (about 2 oz.) were moving at 355 meters per second (almost 800 miles per hour, a bit faster than the speed of sound), and it hit a bowling ball that weighed 4.5 kg (about 10 lbs.), the bowling ball would roll away at 4.5 meters per second (about 10 mph)! Through the collision, the momentum of the little bb moving very fast is transferred to the bowling ball, which moves slower because it has much more mass!

Collisions cause momentum to move from one object to another object. In everyday life, collisions occur all over the place — pool games, traffic accidents, rubber balls bouncing, baseballs being hit by bats, and more. You can probably observe many collisions just by looking around a classroom. Understanding momentum gives engineers an insight to understand different kinds of collisions. This understanding can help make cars safer, predict the results of two objects bumping into each other, or examine the evidence of a traffic accident.

There are different kinds of collisions. Sometimes objects bump into each other then bounce away from each other, such as when a rubber ball hits the ground. Engineers call this kind of collision an elastic collision. Other times, objects that bump in to each other stick together, such as when a ball of play dough hits the ground – splat! Engineers call these kinds of collisions inelastic collisions. Most of the time, collisions are part elastic and part inelastic. For example, when a shopping cart hits a car, it might dent the car (an inelastic collision), but it also bounces off of the car (an elastic collision). We can learn more about momentum by examining different types of collisions.

When pool balls collide, no momentum is lost. This is called an elastic collision. copyright

An example of a "perfect" elastic collision would be if you dropped a rubber ball on a hard sidewalk and it bounced back to its original height. In real life, balls do not bounce back all the way up to their original height because they lose some of their energy when they hit the ground. This energy may be lost through the creation of a noise (boing!) or through a very small change in temperature (due to the release of energy when the ball collides with the floor). Another example of an elastic collision is when two balls bump into each other on a pool table. In this case, the balls do not stick together — they bounce off each other, even though some energy is lost when the balls make a noise.

An inelastic collision occurs when objects bump into each other and stick together. An example is when two train cars are getting hooked together. The engine of the train pushes one car until it bumps into another car and they hook together. Then, the two cars roll away, connected, at a slower speed.

In both elastic and inelastic collisions, the total momentum of all the objects before the collision is the same as the total momentum of all the objects after the collision. The fact that momentum is not lost is called the Law of Conservation of Momentum. The Law of Conservation of Momentum helps us predict what happens when things bump into each other. For example, during a pool game, if the 8-ball is hit directly with the cue ball, the cue ball will stop and the 8-ball will roll with as much momentum as the cue ball had before the collision. Since the masses of the two balls are the same, this means that the 8-ball will have the same velocity as the cue ball had. If the 8-ball is hit on its side, the two balls will roll in different directions, but with a total combined momentum equal to what the cue ball had before the collision. In other words, even though both balls may be moving, they will move at a slower speed than the cue ball was moving by itself because the cue ball has transferred some of its momentum to the 8-ball.

If momentum is lost in a collision because of noise, breaking glass or bending metal, the collision is called inelastic. copyright

When a fast-moving car hits a telephone pole, there is a tremendous amount of force between the front bumper and the pole. The force can be calculated by the force-momentum relationship:

Why would engineers be interested in this relationship? One reason is to make cars in accidents be safer for people. This relationship says that if momentum is transferred over a longer period of time, there is less force involved. If the force of a collision can be reduced, the chances that someone would get hurt in an accident are lower. Therefore, if engineers can figure out a way to increase the time required for a car to come to a stop in a collision, they can lower the forces that will impact people riding in the car, and the people will be less likely to be hurt. In fact, during the many years of car design, engineers have been very successful in accomplishing this! Older cars were built more solidly than today's cars; their front ends would not crumple in an accident. When an older car ran into something solid, it stopped very quickly, and so both the driver and the car experienced a large impact. Engineers have designed newer cars to crumple on impact, lengthening Δt and thus reducing the force experienced by the occupants. You could say that newer cars are safer in accidents than older cars because of an understanding of the force-momentum relationship.