Newton's Three Laws of Motion:
Isaac Newton's Laws of Motion are three principles upon which Newtonian Mechanics is founded. Everything in Newtonian Mechanics may be derived from these three rules. And even though Newton's Laws have been supplanted three times, first by Einstein's Special Relativity replacing Newtonian dynamics, next when Einstein's General Relativity displaced Newton's Gravitation Law, and finally when Quantum Mechanics overthrew the determinism of Newtonian dynamics, everyday life is still ruled for the most part by Newtonian Mechanics. For instance, engineering, construction, buildings and bridges, are all based upon Newtonian Mechanics. Why, we even placed men on the Moon using only Newtonian Mechanics! Einstein's Theories of Relativity were not needed to fly humans to the Moon nor, for that matter, to send the Cassini-Huygens robotic spacecraft to Saturn.
We will have numerous occasions to use these three rules when discussing our FPF demonstrations.
(I) A body in linear motion will stay in linear motion unless acted upon by an unbalanced force. A body at rest will remain at rest unless acted upon by an unbalanced force.
(II) An unbalanced force acting on a body produces a change in its momentum: F = dp/dt. This is what Newton actually said, but today you more commonly see this written as F = ma, that is, the unbalanced force produces a change in the acceleration, a, of the body.
(III) For every action there is an equal and opposite reaction.
- (I) Did you know that Newton's First Law was actually due to Galileo and not Newton? Galileo was a superb experimentalist, really he was what might be considered the first true scientific experimentalist in that he performed experiments from which he abstracted physical principles. Galileo was the first to recognize that he needed to "idealize" his experiments. For instance, he observed various things rolling down inclined planes and recognized that there was a certain amount of friction that made the measurements not precisely match what the mathematics said it should be. Before Galileo, the Aristotelean view was that the natural state of things is to come to rest, that all Earthly things eventually come to rest while heavenly bodies do not. Galileo realized that Earthly objects also would not come to rest if there was no friction.
So Galileo recognized that a wheel rolling down an inclined plane, the steeper the incline the greater the acceleration of the wheel. Galileo then made the incline very shallow, just barely downhill, and now his wheel's acceleration was very slight but still positive (increasing the speed of the wheel). Galileo then did a very clever experiment, he made his incline plane slope slightly uphill. Now when he rolled the wheel on the slightly uphill incline, he noticed that the wheel now slightly decelerated (decreasing the speed of the wheel), that is, the acceleration had become slightly negative. Galileo's genius next came into play. He reasoned that if a slight downhill slope produced a small positive acceleration while a slight uphill slope produced a small negative acceleration, then a zero slope (horizontal) would produce a zero acceleration (no change in the speed of the wheel). Galileo recognized that his real world wheel suffered from friction and thus it would eventually slow down because of the friction, but he reasoned that without the friction, that is, for an idealized wheel, then once it was in motion it would continue in motion at the same speed forever.
Newton's First Law defines the construct known as an Inertial Frame of Reference. Any observer who is moving at a constant velocity with no external forces acting upon the observer is said to be in an inertial frame of reference.
- (II) According to Newton's Second Law of Motion, a force twice as large will produce an acceleration twice as great. And a mass twice as large will produce one-half the acceleration for the same force.
Say John weighs 100 pounds, Jim weighs 100 pounds, and Jane weighs 50 pounds. All three are standing in their speed skates on the ice at the Roosevelt rink. If John and Jim face each and John pushes hard against Jim, what happens? Yup, that's right, both head off backwards in opposite directions at identical speeds. What would happen if John stood still and Jim pushed hard against John? Once again, both John and Jim would move off backwards at the same speed in opposite directions. What would happen if John and Jim both shoved off each other's hands? Then both would move off backwards but with twice the speed as when only one was pushing. And what would happen if John and Jane were facing each other and John pushed hard against Jane? Then John would move backwards and Jane would move backwards, but Jane would move at twice the speed as John since she weighs half as much!
Note that the F=ma form for Newton's Second Law assumes that the mass m is a constant, and, as such, is only approximately valid. That is to say, it is extremely accurate, but only for slow velocities. When the velocities approach the speed of light, c, then this law is no longer very accurate; it is not valid for speed approaching c. On the other hand, Newton's original expression, F=dp/dt, is valid even for velocities near light speed when a suitable definition of the momentum p is chosen.
In addition, notice that Newton's version, F=dp/dt, says that if there is no unbalanced force, i.e., F=0, then dp/dt=0 which means that p=constant. We say that the momentum p is conserved if p is a constant.
- (III) Newton's Third Law may not be obvious as the first two. But say you lean your shoulder into your pickup. Obviously your shoulder is applying a force on the pickup. But equally obvious is the fact that the pickup must be applying a force on your shoulder for it is were not then you would fall over. And the force the pickup is applying to your shoulder must be equal but opposite to the force your shoulder is applying to your pickup. If it were somehow greater, then your pickup would cause your shoulder to move away from it. If it were somehow less then your shoulder would make a dent in the side of your pickup.
All of the lines (A --> B, C --> D, E --> F) in this Figure obey Conservation of Linear Momentum.
Notice that in the last line of the above Figure, one steel ball enters from the left at a speed of v (Part A), but two steel balls exit to the right at a speed of v/2 (Part D'). Now the entering ball has momentum p_{enter} = mv while the exiting two balls carry momentum p_{exit}=2m(v/2)=mv. These two momenta are the same, thus the A --> D' line also satisfies Conservation of Linear Momentum. Does it or does it not occur in practice? Why or why not?
Newton's Third Law allows us to extend the concept of Conservation of Momentum from an individual particle via the Second Law to an entire system of particles. It is really this extension capability that makes both the Third Law and the Conservation of Momentum Law so very useful in physics, engineering, space flight, etc.
- History of what the ancients called "Natural Philosophy":
This PDF provides a very quick history of the chief conceptual developments of Classical Mechanics.
- Newton's Laws of Motion:
This PDF introduces Newton's Three Laws of Motion.
- Newton's Third Law and Electrodynamics
Given the importance of the Third Law for Conservation of Momentum, would you be surprised to learn that the Third Law is violated by electrodynamics? Yup, that's right. If you consider two moving charges, the electric and magnetic forces between them are equal but not opposite! Thus momentum is not conserved in this system --- okay, that is a partial fib, mechanical momentum is not conserved, but when we recognize that the resulting electromagnetic field also has momentum, then the total momentum of both the mechanical momentum of the particles and the field momentum of the electromagnetic field is conserved!
The following PDF file explains why mechanical momentum is not conserved:
- Physics uses the Greek Alphabet extensively. Here is a table of the Greek alphabet and common usages:
- Qunatifier Prefixes for SI Units of Measure:
- Here are a few Units of Measure:
- Here are a few Physical Constants:
- Most Physics is expressed in terms of vectors and their generalizations to tensors and differential forms. The following PDF gives a quick review of Vectors:
This provides a concise review of vectors, dot products, the geometric interpretations of dot products, a few dot product properties, and the ever important Cauchy-Schwarz Inequality.
Copyright (c) 2011 Craig G. Shaefer, all rights reserved.
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