# Momentum

The momentum of an object is defined as the mass of the object multiplied by the velocity of the object. Mathematically, that definition can be expressed as p = m · v, where p represents momentum, m represents mass, and v represents velocity.

In many instances, the mass of an object is measured in kilograms (kg) and the velocity in meters per second (m/s). In that case, momentum is measured in kilogram-meters per second (kg · m/s). Recall that velocity is a vector quantity. That is, the term velocity refers both to the speed with which an object is moving and to the direction in which it is moving. Since velocity is a vector quantity, then momentum must also be a vector quantity.

## Conservation of momentum

Some of the most common situations involving momentum are those in which two moving objects collide with each other or in which a moving object collides with an object at rest. For example, what happens when two cars approach an intersection at the same time, do not stop, but collide with each other? In which direction will the cars be thrown, and how far will they travel after the collision?

The answer to that question can be obtained from the law of conservation of momentum, which says that the total momentum of a system before some given event must be the same as the total momentum of the system after the event. In this case, the total momentum of the two cars moving toward the intersection must be the same as the total momentum of the cars after the collision.

Suppose that the two cars are of very different sizes, a large Cadillac with a mass of 1,000 kilograms and a small Volkswagen with a mass of 500 kilograms, for example. If both cars are traveling at a velocity of 10 meters per second (mps), then the total momentum of the two cars is (for the Cadillac) 1,000 kg · 10 mps plus (for the Volkswagen) 500 kg · 10 mps = 10,000 kg · mps + 5,000 kg · mps = 15,000 kg · mps. Therefore, after the collision, the total momentum of the two cars must still be 15,000 kg · mps.

## Applications

A knowledge of the laws of momentum is very important in many occupations. For example, the launch of a rocket provides a dramatic application of momentum conservation. Before launch, the rocket is at rest on the launch pad, so its momentum is zero. When the rocket engines fire, burning gases are expelled from the back of the rocket. By virtue of the law of conservation of momentum, the total momentum of the rocket and fuel must remain zero. The momentum of the escaping gases is regarded as having a negative value because they travel in a direction opposite to that of the rocket's intended motion. The rocket itself, then, must have momentum equal to that of the escaping gases, but in the opposite (positive) direction. As a result, the rocket moves forward.

[ See also Conservation laws ; Mass ; Laws of motion ]