Chapter Goal: To introduce the fundamental concepts of motion.

1
Chapter 1 Concepts of Motion
Pickup PSE3e Photo from page 2, snowboarder jump.

• Chapter Goal To introduce the fundamental
  concepts of motion.

Slide 1-2
2
Chapter 1 Preview
Slide 1-3
3
Chapter 1 Preview
Slide 1-4
4

• Four basic types of motion

Slide 1-19
5
Making a Motion Diagram

• Consider a movie of a moving object.
• A movie camera takes photographs at a fixed rate
  (i.e., 30 photographs every second).
• Each separate photo is called a frame.
• The car is in a different position in each frame.
• Shown are four frames in a filmstrip.

Slide 1-20
6
Making a Motion Diagram

• Cut individual frames of the filmstrip apart.
• Stack them on top of each other.
• This composite photo shows an objects position
  at several equally spaced instants of time.
• This is called a motion diagram.

Slide 1-21
7
Examples of Motion Diagrams

• An object that has a single position in a motion
  diagram is at rest.
• Example A stationary ball on the ground.
• An object with images that are equally spaced is
  moving with constant speed.
• Example A skateboarder rolling down the sidewalk.

Slide 1-22
8
Examples of Motion Diagrams

• An object with images that have increasing
  distance between them is speeding up.
• Example A sprinter starting the 100 meter dash.
• An object with images that have decreasing
  distance between them is slowing down.
• Example A car stopping for a red light.

Slide 1-23
9
Examples of Motion Diagrams

• A motion diagram can show more complex motion in
  two dimensions.
• Example A jump shot from center court.
• In this case the ball is slowing down as it
  rises, and speeding up as it falls.

Slide 1-24
10
Position and Time

• In a motion diagram it is useful to add numbers
  to specify where the object is and when the
  object was at that position.
• Shown is the motion diagram of a basketball,
  with 0.5 s intervals between frames.
• A coordinate system has been added to show (x,
  y).
• The frame at t ? 0 is frame 0, when the ball is
  at the origin.
• The balls position in frame 4 can be specified
  with coordinates (x4, y4) ? (12 m, 9 m) at time
  t4 ? 2.0 s.

Slide 1-31
11
Position as a Vector

• Another way to locate the ball is to draw an
  arrow from the origin to the point representing
  the ball.
• You can then specify the length and direction of
  the arrow.
• This arrow is called the position vector of
  the object.
• The position vector is an alternative form of
  specifying position.
• It does not tell us anything different than the
  coordinates (x, y).

Slide 1-32
12
Tactics Vector Addition
Slide 1-33
13
Vector Addition Example Displacement
Sam is standing 50 ft east of the corner of 12th
Street and Vine. He then walks northeast for 100
ft to a second point. What is Sams change of
position?

• Sams initial position is the vector .
• Vector is his position after he finishes
  walking.
• Sam has changed position, and a change in
  position is called a displacement.
• His displacement is the vector labeled .

Slide 1-34
14
Definition of Displacement

• The displacement of an object as it moves
  from an initial position to a final position
  is
• The definition of involves vector
  subtraction.
• With numbers, subtraction is the same as the
  addition of a negative number.
• Similarly, with vectors

Slide 1-35
15
Tactics Vector Subtraction
Slide 1-36
16
Time Interval

• Its useful to consider a change in time.
• An object may move from an initial position
  at time ti to a final position at time tf.

A stopwatch is used to measure a time interval.

• Different observers may choose different
  coordinate systems and different clocks, however,
  all observers find the same values for the
  displacement ? and the time interval ?t.

Slide 1-41
17
Average Speed, Average Velocity

• To quantify an objects fastness or slowness, we
  define a ratio
• Average speed does not include information about
  direction of motion.
• The average velocity of an object during a time
  interval ?t, in which the object undergoes a
  displacement ? , is the vector

The victory goes to the runner with the highest
average speed.
Slide 1-42
18
Motion Diagrams with Velocity Vectors

• The velocity vector is in the same direction as
  the displacement ? .
• The length of is directly proportional to the
  length of ? .
• Consequently, we may label the vectors connecting
  the dots on a motion diagram as velocity vectors
  .
• Below is a motion diagram for a tortoise racing a
  hare.
• The arrows are average velocity vectors.
• The length of each arrow represents the average
  speed.

Slide 1-43
19
EXAMPLE 1.2 Accelerating Up a Hill
Motion diagram of a car accelerating up a hill.
Slide 1-44
20
Acceleration

• Sometimes an objects velocity is constant as it
  moves.
• More often, an objects velocity changes as it
  moves.
• Acceleration describes a change in velocity.
• Consider an object whose velocity changes from
  to during the time interval ?t.
• The quantity is the change
  in velocity.
• The rate of change of velocity is called the
  average acceleration

The Audi TT accelerates from 0 to 60 mph in 6 s.
Slide 1-45
21
Tactics Finding the Acceleration Vector
Slide 1-46
22
Tactics Finding the Acceleration Vector

• Notice that the acceleration vectors goes beside
  the dots, not beside the velocity vectors.
• That is because each acceleration vector is the
  difference between two velocity vectors on either
  side of a dot.

Slide 1-47
23
Speeding Up or Slowing Down?

• When an object is speeding up, the acceleration
  and velocity vectors point in the same direction.
• When an object is slowing down, the acceleration
  and velocity vectors point in opposite
  directions.
• An objects velocity is constant if and only if
  its acceleration is zero.
• In the motion diagrams to the right, one object
  is speeding up and the other is slowing down,
  but they both have acceleration vectors toward
  the right.

Slide 1-53
24
Tactics Determining the Sign of the Position,
Velocity, and Acceleration
Slide 1-56
25
Tactics Determining the Sign of the Position,
Velocity, and Acceleration
Slide 1-57
26
Tactics Determining the Sign of the Position,
Velocity, and Acceleration
Slide 1-58
27
Position-versus-Time Graphs

• Below is a motion diagram, made at 1 frame per
  minute, of a student walking to school.
• A motion diagram is one way to represent the
  students motion.
• Another way is to make a graph of x versus t for
  the student

Slide 1-65
28
Example 1.7 Interpreting a Position Graph
Slide 1-66
29
Example 1.7 Interpreting a Position Graph
Slide 1-67
30
Example 1.9 Launching a Weather Rocket
Slide 1-74
31
Example 1.9 Launching a Weather Rocket
Slide 1-75
32
Example 1.9 Launching a Weather Rocket
Slide 1-76
33
Example 1.9 Launching a Weather Rocket
Slide 1-77
34
Units

• Science is based on experimental measurements,
  and measurements require units.
• The system of units in science is called le
  Système Internationale dunités or SI units.
• The SI unit of time is the second, abbreviated
  s.
• 1 s is defined as the time required for
  9,192,631,770 oscillations of the radio wave
  absorbed by a cesium-133 atom.
• The SI unit of length is the meter, abbreviated
  m.
• 1 m is defined as the distance traveled by light
  in a vacuum during 1/299,292,458 of a second.

An atomic clock at the National Institute of
Standards and Technology is the primary standard
of time.
Slide 1-78
35
Units

• The SI unit of mass is the kilogram, abbreviated
  kg.
• 1 kg is defined as the mass of the international
  standard kilogram, a polished platinum-iridium
  cylinder stored in Paris.
• Many lengths, times, and masses are either much
  less or much greater than the standards of 1 m, 1
  s, and 1 kg.
• We use prefixes to denote various powers of 10,
  which make it easier to talk about quantities.

Slide 1-79
36
Unit Conversions

• It is important to be able to convert back and
  forth between SI units and other units.
• One effective method is to write the conversion
  factor as a ratio equal to one.
• Because multiplying by 1 does not change a
  value, these ratios are easily used for unit
  conversions.
• For example, to convert the length 2.00 feet to
  meters, use the ratio
• So that

Slide 1-80
37
Assessment

• When problem solving, it is important to decide
  whether or not your final answer makes sense.
• For example, if you are working a problem about
  automobile speeds and reach an answer of 35
  m/s, is this a realistic speed?
• The table shows some approximate conversion
  factors that can be used to assess answers.
• Using 1 m/s 2 mph, you find that 35 m/s is
  roughly 20 mph, a reasonable speed for a car.
• If you reached an answer of 350 m/s, this would
  correspond to an unreasonable 700 mph, indicating
  that perhaps you made a calculation error.

Slide 1-81
38
Significant Figures

• Its important in science and engineering to
  state clearly what you know about a situationno
  less, and no more.
• For example, if you report a length as 6.2 m, you
  imply that the actual value is between 6.15 m and
  6.25 m and has been rounded to 6.2.
• The number 6.2 has two significant figures.
• More precise measurement could give more
  significant figures.
• The appropriate number of significant figures is
  determined by the data provided.
• Calculations follow the weakest link rule The
  input value with the smallest number of
  significant figures determines the number of
  significant figures to use in reporting the
  output value.

Slide 1-82
39
Determining significant figures.
Slide 1-83
40
Tactics Using Significant Figures
Slide 1-84
41
EXAMPLE 1.10 Using significant figures
Slide 1-85
42
Orders of Magnitude and Estimating
Some approximate lengths and masses Distance you
can drive in 1 hour 105 m Distance
across a college campus 1000 m Length of
your arm 1 m Length of your little
fingernail 0.01 m Thickness of a sheet of paper
104 m Small car 1000 kg Large human 100
kg Science textbook 1 kg Apple 0.1
kg Raisin 103 kg

• In many cases a very rough estimate of a number
  is sufficient.
• A one-significant-figure estimate or calculation
  is called an order-of-magnitude estimate.
• An order-of-magnitude estimate is indicated by
  the symbol , which indicates even less precision
  than .

Slide 1-86
43
Chapter 1 Summary Slides
Slide 1-89
44
General Strategy
Slide 1-90
45
General Strategy
Slide 1-91
46
Important Concepts
Slide 1-92
47
Important Concepts
Slide 1-93