Galileo and Inertia

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Galileo and Inertia

• In the early 1600's, the Italian Physicist
  Galileo Galilee
• perfected the concept of modern experimental
  physics
• and made one of the most important discoveries in
  
• history.
• In his experiments, Galileo studied the motion of
  
• objects by rolling balls down wooden inclined
  planes.

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Galileo and Inertia

• Since Galileo knew about friction, he sanded his
• inclined planes and used water and other
  lubricants
• (oils) to reduce the friction. As the friction
  was
• reduced, the ball rolled farther.
• Galileo then did something ingenious. He allowed
  the
• ball to roll up a second plane!!

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Galileo and Inertia
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Galileo and Inertia

• Regardless of the angle of inclination of the
  second
• inclined plane or its distance from the first
  inclined
• plane, the ball always appeared to roll up the
  second
• inclined plane until the ball reached its
  original height.
• If the inclined plane was not as steep, the ball
  would
• simply roll a greater distance. It was as if the
  ball
• somehow remember its starting height!!
• This discovery was contradictory to Aristotelian
• Mechanics!!

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Galileo and Inertia

• Galileo then asked himself a brilliant question!!
• If the inclined plane had an angle of inclination
  of zero
• (i.e. it was horizontal), when would the ball
  reach its
• original height?

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Galileo and Inertia

• Answer It would never reach its original height
  so it
• would never stop!!
• Galileo therefore concluded that the natural
  state of
• motion is not rest!!

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Galileo and Inertia

• Galileo knew that the Earth was a sphere and the
  ball
• appeared to keep rolling along the surface of the
  
• sphere. He also believed that the planets
  including the
• Earth traveled in circular orbits at constant
  speeds
• (uniform circular motion) around the sun.
• Thus, Galileo decided that all objects continue
  in
• uniform circular motion unless a net push or pull
  (i.e.
• force is applied) to the object.

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Galileo and Inertia

• Thus, Galileo was able to explain why objects
  dont fall
• off the Earth as it spins on its axis or rotates
  around
• the sun.
• Although Galileo experiments were brilliant, he
  was
• incorrect about the natural state of motion since
  he
• didnt know about the concept of gravity. Rene
  Descart
• refined Galileos work by stating that the
  natural
• state of motion of an object is a straight line
  at
• constant speed and not a curved path. The concept
  of
• inertia was given its final form by the great Sir
  Isaac
• Newton as Newtons 1st Law.

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Newtons 1st Law of Mechanics

• A particle will continue is a straight line at
  constant
• speed unless acted upon by a net push or pull
  (i.e.
• force).
• The property of a body to continue in a straight
  line at
• constant speed is called Inertia.
• Mass is the measure of a bodys inertia. Thus, a
  2 kilo-
• gram object has twice the inertia of a 1
  kilo-gram
• object.

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Newtons 1st Law of Mechanics

• Newtons 1st Law tells us a couple of things
• The natural state of mater is a straight line at
• constant speed.
• If an object is not moving in a straight line
  and/or if it is speeding up or slowing down then
  a net push or pull must be acting upon the body.

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Newtons 1st Law

• Question 1 Since an apple speeds up as it falls
  to the
• ground, what does Newtons 1st Law say about the
  net
• push or pull on the apple?
• Question 2 When an object is dropped from a very
  
• high place, the object will initially pickup
  speed until it
• reaches some maximum speed (terminal speed) after
  
• which its speed stays constant. What does
  Newtons
• 1st Law say about the net push or pull on the
  object
• once it reaches terminal speed?

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Newtons 1st Law

• Question 3 Why does a spaceship need an engine
  to
• blast off from the Earth or land on the moon, but
  
• not during the trip from the Earth to the Moon?

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Basic Concepts Of Mechanics

• Question How do we describe the location of an
• object?
• Answer We specify its location in terms of an
  agreed
• upon set of directions and by measuring the
  distance
• from the object to some reference (possibly a
  tree).

East
McDonalds
South
TSU Science Building
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Basic Concepts Of Mechanics

• Scientist say that you are specifying your
  coordinate
• axis (i.e. the set of agreed upon directions and
  your
• origin). In this example, we might designate the
• directions x and y as well our reference point
  (origin)
• as the TSU science building.

y
McDonalds
x
TSU Science Building
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Basic Concepts Of Mechanics

• The arrow showing us the location of McDonalds
  is
• called McDonalds position vector.
• A vector is a mathematical quantity that has both
  (size)
• magnitude and direction! You must not only tell
  the
• visitor how far it is to McDonalds, but also the
  
• direction to walk.

y
McDonalds
600 m
20
x
TSU Science Building
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Basic Concepts Of Mechanics

• The mathematics of vectors is very different from
  the
• math of scalars (i.e. regular numbers) which you
  are
• accustomed to using!! It is not 900 m to Sonic
  from the
• Science Building nor do you walk towards
• McDonalds!!

Sonic
300 m
y
McDonalds
600 m
20
x
TSU Science Building
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Basic Concepts Of Mechanics

• Vectors can be added by drawing the vectors to
  scale
• using a ruler and a protractor. This is how
  explorers
• Like Columbus charted their course and is still
  used by
• the Navy today!!
• Example Add the following two vectors using the
• scale 1 cm 1 m.

12 m
10 m
120
30
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Basic Concepts Of Mechanics

• To simplify the math, we will restrict ourselves
  in this
• course to 1-dimensional problems. Thus, we can
• specify the direction of our vectors by the sign
  of our
• answer. For example, the location of Bruners is
• 3000 m and the location of Chamberlain is -1500
  m.

y
3000 m
1500 m
x
TSU Science Building
Chamberlain School
Bruners
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Basic Concepts Of Mechanics

• Question What would be the position vectors for
  the
• following three locations (Chamberlain, Science
• building, and Bruners) using a coordinate system
  
• whose origin was at Chamberlain?

y
3000 m
1500 m
x
TSU Science Building
Chamberlain School
Bruners
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Basic Concepts Of Mechanics

• Note The position of an object is not unique!!
  It always
• depends on your coordinate system. In every
  problem,
• you must first specify your coordinate system and
  then
• determine the position vector for an object!

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Basic Concepts Of Mechanics

• Displacement The displacement of an object is
• defined as the change in the objects position
• vector.
• Displacement (Final Position) (Initial
  Position)
• Question 1 Using the TSU science building
• coordinate system, calculate a students
  displacement
• if they walk from Chamberlain to Bruners.

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Basic Concepts Of Mechanics

• Question 2 Using the Chamberlain coordinate
• system, calculate a students displacement if
  they walk
• from Chamberlain to Bruners.
• How does your answer to question 2 compare to
• question 1?
• Question 3 Repeat the student displacement
• example, but use a coordinate system attached to
  the
• student!! Compare your result to the result for
• Question 2.

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Basic Concepts Of Mechanics

• A student leaves the TSU science building and
  walks
• to Bruners then to Chamberlain and finally
  returns
• back to the Science building. Answer the
  following two
• questions for the students complete trip using
  the TSU
• coordinate system
• Question 4 What is the distance walked by the
• student?
• Question 5 What is the students displacement?