NEWTONIAN PHYSICS

• Starting from law of inertia (René Descartes, Galilei Galilei),
  Isaac Newton developed a new way of looking at nature.
• Principia Mathematica Philosophiae Naturalis (1687)
  (Mathematical Principles of Natural Philosophy):
  based on a small number of concepts and principles, provide a clear and quantitative explanation of a vast array of phenomena.
• give a unification of our view of nature -
  the first major synthesis of science
• explain: motion of bodies on Earth and in heaven
  (falling bodies, Moon, planets, comets,...
• key concepts:
  • velocity
  • acceleration
  • force
  • inertial mass, gravitational mass
• key principles:
  • law of inertia ("Newton's 1st law of motion")
  • law of motion (forces) (Newton's "2nd law of motion")
  • law of force pairs (action=reaction)
    ("Newton's 3rd law of motion")
  • law of gravity

FORCE

• LAW OF INERTIA: no force no acceleration;
• if acceleration - there must be force;
• we say: body exerts force on another if it forces the other body to accelerate;
• note there is some circularity in this definition, but definition is justified by its usefulness and predictive power;
• force is not a property of a body;
• if more then one force acting effects add
  forces add -- "net force";
• acceleration is in direction of net force;
• two or more forces can compensate ("balance") each other
  (e.g. two equally stron forces acting in opposite directions)

• kinds of forces:
  • push, pull, shove, kick, tap
  • friction, air resistance
  • gravity
  • electric
  • magnetic

• Aristotelian view:
  forces cause velocity (force necessary to maintain uniform motion)
• Newtonian view:
  forces cause acceleration (force necessary to change motion)

• Observations:
  • stronger force larger acceleration
  • more ``massive'' object smaller acceleration
  • apply more than one force net force determines acceleration
• inertia = resistance of object against being accelerated;
  
• (inertial) mass = measure of amount of inertia,
  observed to be proportional to amount of matter - set them equal;
  unit of mass = kilogram = kg
  (original definition: = mass of 1 liter of water)
• observations can be summarized by:

  

  (F = force, a=acceleration, m= mass )

  

• by appropriate choice of units, can make
  (i.e convert ``proportional'' into ``equal'')
• Newton's 2nd law:

  

• but F,a are vectors, and acceleration is in direction of force

  

• unit of force = newton
  1 newton
  in English system: unit of force = pound = 4.448 N
• note: the mass in Newton's 2nd law is the "inertial mass"

WEIGHT

• weight of an object
  = net gravitational force on an object
• weight mass:
  • mass of object = quantity of its inertia;
  • weight of object = force on it due to gravity;
    depends on environment;
  • our weight on the Moon is 1/6 of that on the surface of the Earth;
  • our weight on a high mountain is smaller than at sea level;
  • our weight in a satellite in orbit around Earth = 0;
  • our mass is always the same.
• example: book resting on table:
  book attracted to Earth by gravitational force;
  book exerts force (= its weight) on table;
  table exerts equal and opposite force on book
  ("contact force","perpendicular force", "normal force")
  net force on book = 0 book stays at rest on table
  (does not fly away, does not fall through table)

Law of force pairs (action and reaction)
("Newton's 3rd law":)
when a body exerts a force on a second body, the second body exerts an equally strong force on the first body, directed opposite to the first force
"actio = reactio"

examples:

• apple and Earth:
  • Earth exerts force on apple apple exerts force on Earth;
  • Earth's large mass
    Earth's acceleration very (unmeasurably) small
• book on table: 2 pairs of forces:
  • Earth exerts gravitational force on book,
  • book exerts gravitational force on Earth.
  • book exerts force on table,
  • table exerts force on book ("contact force")
  • contact force exerted by table on book compensates gravitational force of Earth on book book stays put
    (contact force caused by interaction of electrons in atoms of book with those in table)
• walking: exert force on ground ground exerts force on you
• rowing, driving,
• recoil of a gun,
• rocket propulsion

KEPLER's LAWS

(Johannes Kepler, 1571 - 1630)

1. The orbit of a planet around the Sun is an ellipse with the Sun at one focus.
2. A line joining a planet and the Sun sweeps out equal areas in equal times.
3. The squares of the revolution periods of the planets are proportional to the cubes of their distance from the Sun:

   

   K = proportionality constant;

Notes:

• Ellipse = locus of points for which the sum of the distances from two fixed points (the focal points, or "foci") is constant, = 2a,
  where a = semimajor axis of the ellipse
• distance in 3rd law is really semimajor axis
• a circle is a special case of an ellipse, where the semimajor and semimajor axes are equal: a = b = r
• excentricity of ellipse =
  (distance of focus from center) divided by (semimajor axis)
• excentricity of a circle = 0
• excentricities of most planetary orbits very small (except Pluto)

GRAVITATION

• material bodies have a property called GRAVITATIONAL MASS; due to this property, they can exert a force (GRAVITATIONAL FORCE) on other bodies that also have this property.
• the force is attractive and acts along the line connecting the two bodies.
• the force acts without physical contact between the bodies ("action at a distance")
• Newton's law of gravitation:
  Between any two objects there acts an attractive force that is proportional to the product of the two objects' masses and inversely proportional to the square of the distance between the two objects:

  

  the "proportionality constant" G is called "gravitational constant";

• it turns out that gravitational mass is proportional to inertial mass - set them equal (this fixes value of gravitational constant)

  

  distance d = the distance between the "centers of mass" (centers of gravity) of the two objects

• note that gravitational force is a very weak force:
  gravitational force between two football players (assume mass = 100kg each) at 1 ft distance is about newtons pounds!