Newton's first law
The methods of analyzing space, time and motion described in the previous several lectures are called kinematics. Galileo rightly deserves much of the credit for developing these methods. [Although there are many other things that he gets credit for which are probably not deserved. See The Sleepwalkers, by Arthur Koestler.] The idea of describing position and velocity as functions of time seems commonplace and natural to use. However, one must understand that in those olden days of yore (around 1600) there were no speedometers, speed limits and photo radar detectors to spoil our fun.Kinematics is only a way of describing motion. There's no "real physics" here. Nevertheless, this system of describing motion was necessary for the "real physics". We will now explore the question "What causes the changes we experience in the world?"
The first bit of progress on this question involves understanding what really constitutes a change. The previous common sense view of the world was summarized by Aristotle's Physics.
The earth is at the centre of the universe. Any change in the position of an object must be measured with respect to that universal centre. All matter is made of four elements: earth, water, air and fire. The natural place for solid materials made of earth is close to the centre, on the ground. Any solid object displaced from its natural place will experience a tendency to return there if the force on it is removed. This tendency of solid objects to return to their natural place in the universe's hierarchy is called "Gravity". Heat, on the other hand, belongs in the heavens along with the sun and stars and other fiery objects. Thus a flame is attracted upward by the tendency for it to reach its natural place. This effect is called "Levity". Matter consisting of the other elements tend to arrange themselves accordingly in the natural hierarchy between earth (down here) and fire (up there). Other forces could only arise from living organisms like horses or humans. (A living force was called "vis vitae".)This sort of explanation seems to wrap up observed phenomena in a neat package consistent with both reason and observation. It conforms to many people's naive understanding of the world. However, it completely lacks predictive ability. Aristotle's physics was sometimes downright wrong and useless to the practical person. Any shipwright trying to design a ship according to Aristotle's principles of buoyancy would end up under water.
May force be with us
When we first think of the "causes of motion" we naturally think of "force". It seems necessary to keep pushing or pulling something in order to keep it moving and pushes and pulls are all called forces. In these modern times we have roller blades and other low-friction bearings which allow us to observe motion with less and less friction. In orbit around the earth, astronauts and cosmonauts easily get used to the idea that once one starts to float away, there's no way back unless some thing or some force opposes the motion. It should be easy for us to get used to the idea that force isn't necessary to maintain motion at constant velocity; nevertheless, that idea is still not entirely natural.
Galileo Plays Ball
Galileo first came to this conclusion while rolling balls down inclined planes. He noticed that balls rolling downhill gain speed, balls rolling uphill lose speed and balls rolling along a horizontal track tend to go on until they have to roll uphill. Imagine that the ball starts out at a fixed height each time, is allowed to roll along a horizontal length and then up an incline until it stops at about the same height at which it started. As the slope of the last incline is lowered, it will have to roll farther and farther along until it comes to a stop at about the same height at which it started.If the incline at the end is lowered all the way until it is horizontal, then one could imagine that it would roll on forever, and ever. Of course it won't really go on forever because little bumps in the track and rough spots on the ball slow it down. What Galileo did was to make an idealization based on real observations and then formulate a principle based on the idealization.
Nowadays we have much better devices for minimizing friction. The dry ice puck described in the textbook is one example. Another is the linear air track. The air track is made of a triangular beam with little holes along the two top sides. When air is blown through the beam and out the holes a little glider can ride on the cushion of air. Of course it has to be level and perfectly straight, but normally it is possible to achieve virtually ideal frictionless motion over several meters' length.Gravity acts on both the dry ice puck and on the air track glider pulling it downwards. The gas upon which they ride acts to counteract the force of gravity by balancing it with a force in the upward direction. It is a sort of "antigravity". When all he forces on the puck are balanced then the puck would stand motionless indefinitely or glide away at a constant velocity until it hits the bumper at the end of the track. In this case we are careful to say there is no net force on the glider or puck. There are indeed forces on it, one up the other down. They cancel out and net to zero.
The conclusion reached from all these sorts of observations and experiments is that an object which is not under the influence of any unbalanced force remains at rest or in motion at constant velocity. This is known as the Law of Inertia. It is also called Newton's First Law of Motion although he didn't really invent it. Galileo said it almost right, Descartes did get it right but Newton usually gets the credit, at least in English textbooks.
We need a fixed frame of reference, or do we?
The earth is no longer the centre of the universe. The frame of reference which we so confidently drew on the blackboard, which was attached to the earth, cannot be considered absolutely at rest. We have already acknowledged that the position of the origin doesn't really matter. All the conclusions about laws of physics don't depend on where we put that origin. However, it would be nice to find a frame of reference which we know is absolutely at rest so that we can talk of true velocities with respect to it..In fact, such a truly motionless frame of reference has not yet been found. But that doesn't really matter. The law of inertia says that constant motion doesn't need a force just like constant rest doesn't. So we will find that all the laws of physics won't depend on whether our frame of reference is moving at constant velocity or not. In other words, all frames of reference are equally valid so long as they are moving at constant velocity. There is really no reason to prefer one such frame over another. Such a frame of reference, moving at constant velocity, is called an "inertial frame of reference". A bus which is lurching around left and right and up and down is not an inertial frame. Objects on a bus appear to accelerate with respect to a coordinate system fixed to the bus even though no net force is applied to them. But stick your coordinate system to a fixed object or one moving constantly and accelerations only occur when forces act and are unbalanced.
Picky, picky, picky
There is a small logical difficulty here. The law of inertia is said to be valid only in so-called "inertial frames of reference". This makes sense. But how do we know if any particular reference frame is indeed inertial? Well, if the law of inertia is obeyed, if nothing accelerates unless net forces pull or push, then the frame of reference must be inertial.
Read that last paragraph again. You should be able to see that this reasoning is circular. "In an inertial frame the law of inertia holds, and if the law of inertial holds in a frame of reference, then it is inertial." Well some basic physics textbooks leave it at that and let the discerning student suspect that physics is bunk. We, on the other hand, will try to resolve the problem here by saying that the law of inertia in fact only states that inertial frames of reference do indeed exist. A practical person will not bother himself or herself too much about these fine logical points. But it is a good idea to examine things that bother our sense of logic. Sometimes major discoveries are waiting in those corners where things don't seem to make sense.
