Science Weblecture for Unit 30

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**Topic area**: Physics: Dynamics (forces)**Terms and concepts to know**: Physical Law, force, mass, acceleration, inertia**See historical period(s)**: Newton's Laws of Motion

**Lecture Outline**

Newton's description of the laws of motion confirmed for European natural philosophers that mathematical analysis was a legitimate way of looking at the universe. Aristotle had separated the methods of mathematics from the methods of natural philosophy in his discussion of *Physics* and *Metaphysics*, and this division of the sciences by their methodologies persisted through the Middle Ages. It was one of the issues Copernicus raised in proposing that his mathematical analysis of the motions of the planets was sufficient support for the adoption of a heliocentric planetary model. Kepler's success in showing that planets had elliptical orbits ruled by empirical laws, and Galileo's success with falling bodies that led to a science of ballistics, caused many to question whether the Aristotelian *divisio scientia* was valid. Newton's publication of the *Principia* firmly established a new, mathematical physics.

Galileo originally stated the law of inertia as *the tendency of a body to remain in a state of rest or travel in a straight line*. Newton realized that "a state of rest" is merely a particular state of motion where velocity is equal to zero. He restated the law of inertia as *the tendency of a body to remain in its particular state of motion (whether rest or actual motion) unless acted on by an outside force*, a slightly more general description of inertia.

You may remember that in our earlier discussions of motion, velocity and acceleration, we defined acceleration as any change in motion in the motion of a body. Such a change can occur in direction or in speed, whether an increase or decrease. The law of inertia says that this change can occur only if we have an outside force acting on the body. This means that a system cannot change its own speed or direction.

Newton's second law explains that the change in motion is proportional to the force exerted on the body. This is usually expressed mathematically as **F** = m**a**. The greater the force, the greater the change in acceleration. You can also look at this from the opposite perspective: to achieve greater acceleration, you need a bigger force.

Force is also dependent on the mass of the object: the greater the mass, the greater the force required to change its velocity. This explains what happens with Galileo's falling balls of different masses. While they undergo the same acceleration in falling the same distance in the earth's gravitational field, the more massive ball strikes the ground with greater force.

The third law explains the interaction between two bodies when a force is applied. You push on the chair with your hand, and you feel the chair. This pressure is the chair pushing back on your hand. If you push harder, the (unmoving) chair pushes back harder -- that is, it exerts *an equal and opposite reaction (force)* to the force of your hand.

Review the chapters on velocity (2) and acceleration (3) if you need to, then read about Newtonian mechanics (chapter 4) up to the section on Gravity (we'll cover that topic later) at the Learn Physics Today! site. This site proves a basic introduction to physics by teaching a definition and having you use it immediately. I strongly encourage you to try as many of the checkpoint problems as possible to make sure that you understand the concepts.

- What is the law of inertia? [What happens to a body in motion if no forces act on it? What happens to a motionless body if no forces act on it?]
- Why is determining the instantaneous rates of change difficult?
- What are the subjects of study in dynamics, statics, and mechanics?
- What is velocity?
- What is acceleration?
- What is friction?
- Explain each of the terms in the formula
*d = vt + d*_{0}. - Explain each of the terms in the formula
*s = 1/2 at*^{2}+ s_{0}. - What is Newton's first law? What does it mean?
- What is Newton's second law?
- What is Newton's third law? Give an example of how it works.

Suppose we now try to see how this works with a rocket in space. We launch our rocket using a reaction combining hydrogen and oxygen gasses, which produces water (a nice, clean "waste" product that can rain harmlessly back to earth) and a lot of kinetic energy of motion, which propels the water one way and the rocket the other way.

But wait: we said in the law of inertia that an object can't change its motion unless acted on by an outside force. The gases are inside the rocket, so why isn't the acceleration of the rocket a violation of the law of inertia?

To understand what is happening, we have to look at the rocket and the expelled gases as components of a *system* that remains a system even if the components move away from each other. This system has a center of mass. It is the motion of the whole system, which we can define mathematically as concentrated in the center of mass, that must follow Newton's laws. While the rocket moves in one direction, the gases move in the opposite direction. If we add up all the changes in motion of all the components, the net change is **zero**. The center of mass is **not** accelerated, so the law of inertia holds.

When we **do** apply an outside force to an object, one of two things may happen.

- If the force is applied along a line that passes through the object's center of mass, the object will change location as its center of mass moves through space with increasing (or decreasing) speed. (Translational motion)
- If the force is applied along a line that does NOT pass through the object's center of mass, the object will
**rotate**around its center of mass with increasing (or decreasing) speed. (Rotational motion)

Try this with a pencil or round dowel -- chose something that does not have flat sides but will roll freely.

- You can find the center of mass by trying to balance the pencil on your finger. Mark this point on the pencil.
- With your finger or another pencil, push on the center of mass point. What happens?
- Place the pencil on a level, flat, smooth surface so that it is free to roll but won't start rolling on its own.
- With your finger or another pencil, push on one end of the pencil. What happens?

- What is a physical law?
- Are there ever exceptions to physical laws?
- How does a hypothesis or theory become a physical law?
- What is force?

- There are many good introductory sites on physics. The Physics Classroom on Newton's Laws of Motion covers the definition and application of the three laws of motion with diagrams and animations. Its animations from the Multimedia Physics Studios are often amusing as well as demonstrative of the basic principles.
- Use the Interactive activity on Newton's Third Law to explore equal and opposite reactions. This activity also helps you learn how to read about scientific ideas.

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