Puoh Share See's List: History Of Motion

• Newton's Three Laws
  of Motion

• Newton's First Law of Motion:

    

  I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
• we recognize as essentially  Galileo's concept of inertia, and this is often termed simply the "Law of Inertia".

• Newton's Second Law of Motion:

     

  II. The relationship between an object's mass m, its acceleration a,  and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
• This is the most powerful of Newton's three Laws, because it allows quantitative calculations of dynamics: how do velocities change when forces are applied.
• according to Newton, a force causes only a change in velocity (an acceleration); it does not maintain the velocity as Aristotle held.
• according to Aristotle there is only a velocity if there is a force, but according to Newton an object with a certain velocity maintains that velocity unless a force acts on it to cause an acceleration (that is, a change in the velocity).
• This is sometimes summarized by saying that under Newton, F = ma, but under Aristotle F = mv, where v is the velocity.
• Aristotle's view seems to be more in accord with common sense, but that is because of a failure to appreciate  the role played by frictional forces. Once account is taken of  all forces acting in a given situation it is the dynamics of  Galileo and Newton, not of Aristotle, that are found to be in accord with the observations.

• Newton's Third Law of Motion:

     

  III. For every action there is an equal and opposite reaction.

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• Sir Isaac Newton: The
   Universal Law of Gravitation 
  
• There is a popular story that Newton was sitting under an apple tree, an apple fell on his head, and he suddenly thought of the Universal Law of Gravitation. As in all such legends, this is almost certainly not true in its details,  but the story contains elements of what actually happened.
• Newton, upon observing an apple fall from a tree, began to think along the following lines:  The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground.
• Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity", and the associated acceleration the "accleration due to gravity".
• Sir Isaac's Most Excellent Idea
• if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon!
• the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit  around the earth.
• . Suppose we fire a cannon horizontally from a high mountain; the projectile will eventually fall to earth, as indicated by the shortest trajectory in the figure, because of the gravitational force directed toward the center of the Earth and the associated acceleration. (Remember that an acceleration is a change in velocity and that velocity is a vector, so it has both a magnitude and a direction. Thus, an acceleration occurs if either or both the magnitude and the direction of the velocity change.)
• The constant of proportionality G is known as the universal gravitational constant. It is termed a "universal constant" because it is thought to be the same at all places and all times, and thus universally  characterizes the intrinsic strength of the gravitational force.
• The Center of Mass for a Binary System

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• As early as 200 B.C. the Chinese had devised a clever method for solving systems of two linear equations with two unknowns. The method is illustrated in Chapter 7 of the Jiuzhang suanshu (Nine Chapters in the Mathematical Art), one of the earliest surviving mathematical texts from China.
• One pint of good wine costs 50 gold pieces, while one pint of poor wine costs 10. Two pints of wine are bought for 30 gold pieces. How much of each kind of wine was bought?
• Linear Systems in Europe - Cramer's Method
• n 1750, Gabriel Cramer (1704-1752) published the famous rule for solving systems of linear equations that bears his name

• he rule appears in his Introduction to the Analysis of Algebraic Curves and deals with the problem of finding the equation of an algebraic plane curve passing through some fixed points.

   

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