Science 122 Program 18 Momentum & Conservation

# Momentum & ConservationProgram 18Lesson 3.3

## Coming Up

Before we are done with this lesson we will have seen how we can view Newton's laws in a different way which allows us to see relationships which were hidden before. We will also learn about impulse and momentum and the importance of conservation principles.

## 1. Introduction

This lesson begins the rapid expansion of scientific understanding as the Newtonian paradigm was applied in new ways to new situations.

It is not that momentum is significant in and of itself which concerns us. It is that the concept of conservation, specifically the fact that Newton's laws are axiomatic and can be viewed from a different perspective. It is also significant that we can view the physical universe in such an abstract, yet also quantitative way.

Momentum is only one of several physical quantities which is conserved. In this lesson we will see how this works in several situations and set the stage for our understanding of work and energy in the next lesson.

## 2. The swinging ball problem

The problem with the swinging balls is that there is no explanation that can adequately describe their behavior. Aristotle would have been driven mad trying to give an animistic explanation.

We assume that the balls must follow Newton's laws, but it is difficult to see exactly how to apply them. We cannot easily measure the forces involved in the collison, nor can we measure the acceleration since it appears to be nearly instantaneous.

## 3. Second Law Revisited

Fortunately, Newton's laws are good laws, that is the are applicable in virtually any situation. We can go back to the laws and re-examine them, taking a new perspective. In doing so, we will develop an important new concept, that of a conservation law. This will turn out to serve us very well, although in practice, conservation of momentum will not have much use.

## 4. Momentum defined: mass times velocity

When momentum is defined this way, as Newton defined it, "the quantity of motion", it becomes apparent that the force required to stop a moving mass depends on its momentum, not on the mass or the velocity alone.

## 5. Impulse defined: force times time

Now it should be apparent that we do not need to know the acceleration in order to talk about forces. In fact, we do not even need to know the time involved in the force. What we do need to know is that a force applied over a time will cause a change in momentum. In fact, if the mass is constant (as it is in many cases) all we need to deal with is the change in velocity.

## 6. Conservation of Momentum

Now we are ready to approach the idea of conservation. By this we do not mean "conserve" as "to use sparingly". In this context "conservation" means that something remains unchanged. In this section we will explore that concept and its applications in physics.

## 7. Implications and Importance of Conservation of Momentum

Although conservation of momentum has only limited practical usefulness, if any in our everyday world, it is important to our study of the heritage of ideas for several reasons.

## 8. Conservation of Angular Momentum

Although our discussion so far has been limited to motion in one dimension, it is equaly applicable to motion in two or three dimensions. The video program shows several demonstrations of conservation of angular momentum. You might want to think about other applications in the world around you.

## 9. Swinging Balls revisited

Now we are ready to go back to the swinging balls and examine their behavior in light of our conservation law.

We will see that, although conservation can be used to partially explain their behavior, it is not sufficient in and of itself to explain it completely. For that we will need to understand conservation of energy, the topic of the next program.

## 10. Summary

In this lesson we have seen how Newton's laws can be viewed from another perspective to understand the behavior of matter in situations where the forces and accelerations are unspecified or unmeasurable.

We saw howthe concept of conservation of momentum is related to symmetry, and how it can predict the behavior of many kinds of interactions, from collisions and explosions, to the motion of the planets in their elliptical orbits.

We also saw that conservation of momentum alone is necessary but not sufficient to explain the behavior of the "swinging balls."

In future programs we will rely heavily on the conservation concept as it has become one of the central concepts in all of physical science.