1. What is science?
2. How is it done these days?
3. The origins of modern science.
4. Laws of motion, gravity.

1. 3 laws of motion (know them)
2. 2 types of motion, 1) Uniform motion, 2) Acceleration.
3. force
4. What does the 1st law tell us?
5. What does the 2nd law tell us?
6. F = ma
7. Mass
8. Newton’s law of universal gravitation
9. The apple story
10. Halley’s comet
 

• If it was Kepler who initiated modern science, then Newton defined it.
• Newton (1642-1727) was one of the most brilliant people ever. He determined the laws of motion that are still used today to put satellites into orbit, men on the moon, shoot billiards, examine how atoms vibrate, etc. He invented calculus in order to do the math required to compute these things. Newton was a renaissance man.
• There are 3 laws of motion:
1. A moving object will continue moving in a straight line at constant speed and a stationary object will remain at rest, unless acted upon by an unbalanced force.
2. The acceleration produced on an object by a force is proportional to the magnitude of the force and inversely proportional to the mass of the object.
3. For every action there is an equal and opposite reaction.

A moving object will continue moving in a straight line at constant speed and a stationary object will remain at rest, unless acted upon by an unbalanced force.

• It seems obvious, if you leave an object alone then it will not change its state of motion.
• But this was a new idea. From the time of the Greeks until Newton, everyone thought that objects move in circles, unless disturbed, because the circle is the most perfect of paths. Also, is that not how the stars and planets move?
• Newton observed that if you want to move an object in a circle then you must apply some sort of force, otherwise it goes in a straight line. Eg. Swing something around your head on a string and then let it go.
• This leads to two types of motion:
Uniform motion: straight line at constant speed,
Acceleration: all other types of motion, including changes in speed or direction.
• The first law means that if we see acceleration then there must be something that caused it to happen. We call this something: "force".
• Force: something that causes acceleration.
• Inertia: the tendency for an object to remain in uniform motion. If it is at rest then it stays at rest, if it is moving then it remains moving at the same velocity.
• This law tells us how to determine if a force is acting upon an object.

The acceleration produced on an object by a force is proportional to the magnitude of the force and inversely proportional to the mass of the object.

• This law tells us what will happen when a force is applied to an object.
• The change in the velocity of an object, (its acceleration) depends upon two things, 1) how hard you apply force and 2) how massive the object.
• Eg. You can lift a golf ball more easily than a bowling ball.
• Eg. You can throw a golf ball faster than a bowling ball.
• Eg. Less force is required to lift a light object than a heavy one.
• Eg. You can throw a light object faster than a heavy one.
• F = ma, or a=F/m
• m = mass. This is a measure of the amount of matter in an object, for instance, and is determined by the number of atoms that make up the object. It is not a measure of the density.
• The first law is a qualitative law, the second is quantitative.

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Third Law

For every action there is an equal and opposite reaction.
 
• This means that if you apply a force onto something, then it applies the same force back. Eg. If you push on a wall then you feel the force on your hand, as it pushes back. Note that you do not feel the force that you have applied.
• This is a tough law to visualize.
• Because of this law we can say: "I hit his fist with my nose."
• Billiards offers a good example, with balls bouncing off each other.
• So remember that forces act in pairs, going both ways. Eg. Sit on a chair, your weight offers force on the chair, but an opposite force, (imparted by the strength of the chair), holds you up.

• Every motion in the universe involves the interplay of Newton’s laws. Even though there are 3 laws, their effects are felt at the same time, in varying degrees, in every example of any type of motion.
• However, Newton’s laws say nothing about the nature of the forces involved. Most of the work done since figuring out the details about the laws of motion has been about the nature of the natural forces.

• Gravity is one of the most obvious forces that are part of our lives. It keeps us on earth.
• Galileo studied its properties. But he, and all the others believed that gravity was a local phenomenon, working only at the surface of the earth. What else could they think?
• Newton demonstrated that it was a universal thing. People always talk about Newton and the apple. We say that he was sitting in an orchard and an apple hit him on the head and he went “ah ha, gravity”. But it was not really that way. What happened is that he was in the orchard and was watching the moon, wondering why it stayed there up in the sky. In the foreground, he saw an apple fall off the tree. This was when he went “ah ha”. Something held the apple up in the tree, some sort of force. This force was due to the strength of the stem holding the apple to the branch. The apple grew till the strength of the stem could no longer resist the force of gravity and so the apple fell. However the moon does not fall (it does not change its mass). Nor does it fly away, but instead it orbits the earth, accelerating in a circle (actually, an ellipse). This means that there is force acting upon it. The force is the same as that which caused the apple to fall – gravity.
• He then realized that gravity was not a localized force but its effects must be felt throughout the universe, holding the moon in orbit around the earth, holding the planets around the sun, etc.
• This led to Newton’s law of universal gravitation.
• The force of gravity was the first of the natural forces to be understood to some degree.

• Between any two objects, anywhere in the universe, there is an attractive force that is proportional to the masses of the two objects and inversely proportional to the square of the distance between them.
• What does this mean?
• The more massive the objects then the stronger the force.
• The further away from each other then the weaker the force, but this falls as r². This can be understood simply by geometry. Surface area of a sphere is 4pr². As you move further from the surface of the sphere then the area of an angular cross-section is larger by the square of the distance moved. So the same amount of force is now being distributed over a larger area and so it has a weaker effect.

• The equation is

where G is called the generalized gravitational constant.
• The force of gravity is small between small objects but it is very significant between large objects.
  E.g. 1. The solar system was formed because of the force of gravity. The asteroid belt was once a planet that was torn apart by the gravitational pull of the sun in one direction, and the gravitational pull of Jupiter in the other direction.
  E.g. 2. The gravitational pull of the moon causes the tides.
• When you stand on a scale, the force of gravity pulls you down, causing a spring to twist and shorten. The spring has been calibrated to show the correct value of your weight relative to the amount of torsion it undergoes. On the moon, with 1/6th the mass of the earth, the pull on the spring will be 1/6th as much as here, so, on the moon you would weigh 1/6th of the weight measured on Earth. Note that your mass does not change, since you did not lose any atoms.
• How strong is the force? Strong enough that you can only jump 1-3 feet in the air to oppose it.
• We now understand the forces that cause the planets to rotate about the sun.
• The prediction of Halley’s comet in 1758 convinced everyone that Newton was right, 30 years after his death.

• People thinking about the universe that Newton painted have devised a lot of philosophy.
• His universe was ordered and quite predictable. In fact, if you knew where every object was, and their current velocities and the forces then you could predict every possible arrangement for all time. This led people to think that the universe and its events were predestined.