1. The Branches of Physics
Chapter 1
Section 1 What Is Physics?
The Branches of Physics
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2. The Branches of Physics
Chapter 1
Section 1 What Is Physics?
The Branches of Physics

3. Chapter 1
Section 1 What Is Physics?
Physics
The goal of physics is to use a small number of basic concepts, equations, and assumptions to describe the physical world.
These physics principles can then be used to make predictions about a broad range of phenomena.
Physics discoveries often turn out to have unexpected practical applications, and advances in technology can in turn lead to new physics discoveries.

4. Physics and Technology
Chapter 1
Section 1 What Is Physics?
Physics and Technology

5. Chapter 1 The Scientific Method
Section 1 What Is Physics?
The Scientific Method
There is no single procedure that scientists follow in their work. However, there are certain steps common to all good scientific investigations.
These steps are called the scientific method.

6. Chapter 1 Models Physics uses models that describe phenomena.
Section 1 What Is Physics?
Models
Physics uses models that describe phenomena.
A model is a pattern, plan, representation, or description designed to show the structure or workings of an object, system, or concept.
A set of particles or interacting components considered to be a distinct physical entity for the purpose of study is called a system.

7. Chapter 1 Hypotheses Models help scientists develop hypotheses.
Section 1 What Is Physics?
Hypotheses
Models help scientists develop hypotheses.
A hypothesis is an explanation that is based on prior scientific research or observations and that can be tested.
The process of simplifying and modeling a situation can help you determine the relevant variables and identify a hypothesis for testing.

8. Chapter 1 Hypotheses, continued
Section 1 What Is Physics?
Hypotheses, continued
Galileo modeled the behavior of falling objects in order to develop a hypothesis about how objects fall.
If heavier objects fell faster than slower ones,would two bricks of different masses tied together fall slower (b) or faster (c) than the heavy brick alone (a)? Because of this contradiction, Galileo hypothesized instead that all objects fall at the same rate, as in (d).

9. Chapter 1 Preview Numbers as Measurements Dimensions and Units
Section 2 Measurements in Experiments
Chapter 1
Preview
Numbers as Measurements
Dimensions and Units
Accuracy and Precision
Significant Figures
Vectors
Distance/Displacement Speed\Velocity

10. Section 2 Measurements in Experiments
Chapter 1
Objectives
List basic SI units and the quantities they describe.
Convert measurements into scientific notation.
Distinguish between accuracy and precision.
Use significant figures in measurements and calculations.

11. Numbers as Measurements
Section 2 Measurements in Experiments
Chapter 1
Numbers as Measurements
In SI, the standard measurement system for science, there are seven base units.
Each base unit describes a single dimension, such as length, mass, or time.
The units of length, mass, and time are the meter (m), kilogram (kg), and second (s), respectively.
Derived units are formed by combining the seven base units with multiplication or division. For example, speeds are typically expressed in units of meters per second (m/s).

12. Section 2 Measurements in Experiments
Chapter 1
SI Standards

13. Section 2 Measurements in Experiments
Chapter 1
SI Prefixes
In SI, units are combined with prefixes that symbolize certain powers of 10. The most common prefixes and their symbols are shown in the table.

14. Accuracy and Precision
Section 2 Measurements in Experiments
Chapter 1
Accuracy and Precision
Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured.
Precision is the degree of exactness of a measurement.
A numeric measure of confidence in a measurement or result is known as uncertainty. A lower uncertainty indicates greater confidence.

15. Accuracy and Precision
Section 2 Measurements in Experiments
Chapter 1
Accuracy and Precision
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Visual Concept

16. Measurement and Parallax
Section 2 Measurements in Experiments
Chapter 1
Measurement and Parallax
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Visual Concept

17. Chapter 1 Significant Figures
Section 2 Measurements in Experiments
Chapter 1
Significant Figures
It is important to record the precision of your measurements so that other people can understand and interpret your results.
A common convention used in science to indicate precision is known as significant figures.
Significant figures are those digits in a measurement that are known with certainty plus the first digit that is uncertain.

18. Significant Figures, continued
Section 2 Measurements in Experiments
Chapter 1
Significant Figures, continued
Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.

19. Rules for Determining Significant Zeroes
Section 2 Measurements in Experiments
Chapter 1
Rules for Determining Significant Zeroes
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20. Rules for Determining Significant Zeros
Section 2 Measurements in Experiments
Chapter 1
Rules for Determining Significant Zeros

21. Rules for Calculating with Significant Figures
Section 2 Measurements in Experiments
Chapter 1
Rules for Calculating with Significant Figures

22. Rules for Rounding in Calculations
Section 2 Measurements in Experiments
Chapter 1
Rules for Rounding in Calculations
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23. Rules for Rounding in Calculations
Section 2 Measurements in Experiments
Chapter 1
Rules for Rounding in Calculations

24. Chapter 1 Preview Objectives Mathematics and Physics Physics Equations
Section 3 The Language of Physics
Chapter 1
Preview
Objectives
Mathematics and Physics
Physics Equations

25. Section 3 The Language of Physics
Chapter 1
Objectives
Interpret data in tables and graphs, and recognize equations that summarize data.
Distinguish between conventions for abbreviating units and quantities.
Use dimensional analysis to check the validity of equations.
Perform order-of-magnitude calculations.

26. Mathematics and Physics
Section 3 The Language of Physics
Chapter 1
Mathematics and Physics
Tables, graphs, and equations can make data easier to understand.
For example, consider an experiment to test Galileo’s hypothesis that all objects fall at the same rate in the absence of air resistance.
In this experiment, a table-tennis ball and a golf ball are dropped in a vacuum.
The results are recorded as a set of numbers corresponding to the times of the fall and the distance each ball falls.
A convenient way to organize the data is to form a table, as shown on the next slide.

27. Data from Dropped-Ball Experiment
Section 3 The Language of Physics
Chapter 1
Data from Dropped-Ball Experiment
A clear trend can be seen in the data. The more time that
passes after each ball is dropped, the farther the ball falls.

28. Graph from Dropped-Ball Experiment
Section 3 The Language of Physics
Chapter 1
Graph from Dropped-Ball Experiment
One method for analyzing the data is to construct a graph of the distance the balls have fallen versus the elapsed time since they were released. a
The shape of the graph provides information about the relationship between time and distance.

29. Chapter 1 Physics Equations
Section 3 The Language of Physics
Chapter 1
Physics Equations
Physicists use equations to describe measured or predicted relationships between physical quantities.
Variables and other specific quantities are abbreviated with letters that are boldfaced or italicized.
Units are abbreviated with regular letters, sometimes called roman letters.
Two tools for evaluating physics equations are dimensional analysis and order-of-magnitude estimates.

30. Equation from Dropped-Ball Experiment
Section 3 The Language of Physics
Chapter 1
Equation from Dropped-Ball Experiment
We can use the following equation to describe the relationship between the variables in the dropped-ball experiment:
(change in position in meters) = 4.9  (time in seconds)2
With symbols, the word equation above can be written as follows:
y = 4.9(t)2
The Greek letter D (delta) means “change in.” The abbreviation y indicates the vertical change in a ball’s position from its starting point, and t indicates the time elapsed.
This equation allows you to reproduce the graph and make predictions about the change in position for any time.

31. Chapter 3 Preview Objectives Scalars and Vectors
Section 1 Introduction to Vectors
Preview
Objectives
Scalars and Vectors
Graphical Addition of Vectors
Triangle Method of Addition
Properties of Vectors

32. Chapter 3 Scalars and Vectors
Section 1 Introduction to Vectors
Scalars and Vectors
A scalar is a physical quantity that has magnitude but no direction.
Examples: speed, volume, the number of pages in your textbook
A vector is a physical quantity that has both magnitude and direction.
Examples: displacement, velocity, acceleration
In this book, scalar quantities are in italics. Vectors are represented by boldface symbols.

33. Graphical Addition of Vectors
Chapter 3
Section 1 Introduction to Vectors
Graphical Addition of Vectors
A resultant vector represents the sum of two or more vectors.
Vectors can be added graphically.
A student walks from his house to his friend’s house (a), then from his friend’s house to the school (b). The student’s resultant displacement (c) can be found by using a ruler and a protractor.

34. Triangle Method of Addition
Chapter 3
Section 1 Introduction to Vectors
Triangle Method of Addition
Vectors can be moved parallel to themselves in a diagram.
Thus, you can draw one vector with its tail starting at the tip of the other as long as the size and direction of each vector do not change.
The resultant vector can then be drawn from the tail of the first vector to the tip of the last vector.

35. Triangle Method of Addition
Chapter 3
Section 1 Introduction to Vectors
Triangle Method of Addition
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36. Chapter 3 Properties of Vectors Section 1 Introduction to Vectors
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37. Coordinate Systems in Two Dimensions
Chapter 3
Section 2 Vector Operations
Coordinate Systems in Two Dimensions
One method for diagraming the motion of an object employs vectors and the use of the x- and y-axes.
Axes are often designated using fixed directions.
In the figure shown here, the positive y-axis points north and the positive x-axis points east.

38. Determining Resultant Magnitude and Direction
Chapter 3
Section 2 Vector Operations
Determining Resultant Magnitude and Direction
In Section 1, the magnitude and direction of a resultant were found graphically.
With this approach, the accuracy of the answer depends on how carefully the diagram is drawn and measured.
A simpler method uses the Pythagorean theorem and the tangent function.

39. Determining Resultant Magnitude and Direction, continued
Chapter 3
Section 2 Vector Operations
Determining Resultant Magnitude and Direction, continued
The Pythagorean Theorem
Use the Pythagorean theorem to find the magnitude of the resultant vector.
The Pythagorean theorem states that for any right triangle, the square of the hypotenuse—the side opposite the right angle—equals the sum of the squares of the other two sides, or legs.

40. Determining Resultant Magnitude and Direction, continued
Chapter 3
Section 2 Vector Operations
Determining Resultant Magnitude and Direction, continued
The Tangent Function
Use the tangent function to find the direction of the resultant vector.
For any right triangle, the tangent of an angle is defined as the ratio of the opposite and adjacent legs with respect to a specified acute angle of a right triangle.

41. Resolving Vectors into Components
Chapter 3
Section 2 Vector Operations
Resolving Vectors into Components
You can often describe an object’s motion more conveniently by breaking a single vector into two components, or resolving the vector.
The components of a vector are the projections of the vector along the axes of a coordinate system.
Resolving a vector allows you to analyze the motion in each direction.

42. Resolving Vectors into Components, continued
Chapter 3
Section 2 Vector Operations
Resolving Vectors into Components, continued
Consider an airplane flying at 95 km/h.
The hypotenuse (vplane) is the resultant vector that describes the airplane’s total velocity.
The adjacent leg represents the x component (vx), which describes the airplane’s horizontal speed.
The opposite leg represents
the y component (vy),
which describes the
airplane’s vertical speed.

43. Resolving Vectors into Components, continued
Chapter 3
Section 2 Vector Operations
Resolving Vectors into Components, continued
The sine and cosine functions can be used to find the components of a vector.
The sine and cosine functions are defined in terms of the lengths of the sides of right triangles.

44. Adding Vectors That Are Not Perpendicular
Chapter 3
Section 2 Vector Operations
Adding Vectors That Are Not Perpendicular
Suppose that a plane travels first 5 km at an angle of 35°, then climbs at 10° for 22 km, as shown below. How can you find the total displacement?
Because the original displacement vectors do not form a right triangle, you can not directly apply the tangent function or the Pythagorean theorem. d2 d1

45. Adding Vectors That Are Not Perpendicular, continued
Chapter 3
Section 2 Vector Operations
Adding Vectors That Are Not Perpendicular, continued
You can find the magnitude and the direction of the resultant by resolving each of the plane’s displacement vectors into its x and y components.
Then the components along each axis can be added together.
As shown in the figure, these sums will be the two perpendicular components of the resultant, d. The resultant’s magnitude can then be found by using the Pythagorean theorem, and its direction can be found by using the inverse tangent function.

46. Chapter 3
Section 4 Relative Motion
Objectives
Describe situations in terms of frame of reference.
Solve problems involving relative velocity.

47. Chapter 3 Frames of Reference
Section 4 Relative Motion
Frames of Reference
If you are moving at 80 km/h north and a car passes you going 90 km/h, to you the faster car seems to be moving north at 10 km/h.
Someone standing on the side of the road would measure the velocity of the faster car as 90 km/h toward the north.
This simple example demonstrates that velocity measurements depend on the frame of reference of the observer.

48. Frames of Reference, continued
Chapter 3
Section 4 Relative Motion
Frames of Reference, continued
Consider a stunt dummy dropped from a plane.
(a) When viewed from the plane, the stunt dummy falls straight down.
(b) When viewed from a stationary position on the ground, the stunt dummy follows a parabolic projectile path.

49. Chapter 3 Relative Motion Section 4 Relative Motion
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50. Chapter 3 Relative Velocity Section 4 Relative Motion
When solving relative velocity problems, write down the information in the form of velocities with subscripts.
Using our earlier example, we have:
vse = +80 km/h north (se = slower car with respect to Earth)
vfe = +90 km/h north (fe = fast car with respect to Earth)
unknown = vfs (fs = fast car with respect to slower car)
Write an equation for vfs in terms of the other velocities. The subscripts start with f and end with s. The other subscripts start with the letter that ended the preceding velocity:
vfs = vfe + ves

51. Chapter 2 Preview Objectives One Dimensional Motion Displacement
Section 1 Displacement and Velocity
Chapter 2
Preview
Objectives
One Dimensional Motion
Displacement
Average Velocity
Velocity and Speed
Interpreting Velocity Graphically

52. Section 1 Displacement and Velocity
Chapter 2
Objectives
Describe motion in terms of frame of reference, displacement, time, and velocity.
Calculate the displacement of an object traveling at a known velocity for a specific time interval.
Construct and interpret graphs of position versus time.

53. One Dimensional Motion
Section 1 Displacement and Velocity
Chapter 2
One Dimensional Motion
To simplify the concept of motion, we will first consider motion that takes place in one direction.
One example is the motion of a commuter train on a straight track.
To measure motion, you must choose a frame of reference. A frame of reference is a system for specifying the precise location of objects in space and time.

54. Chapter 2 Frame of Reference Section 1 Displacement and Velocity
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55. displacement = final position – initial position
Section 1 Displacement and Velocity
Chapter 2
Displacement
Displacement is a change in position.
Displacement is not always equal to the distance traveled.
The SI unit of displacement is the meter, m.
x = xf – xi
displacement = final position – initial position

56. Chapter 2 Displacement Section 1 Displacement and Velocity
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57. Positive and Negative Displacements
Section 1 Displacement and Velocity
Chapter 2
Positive and Negative Displacements

58. Chapter 2 Average Velocity
Section 1 Displacement and Velocity
Chapter 2
Average Velocity
Average velocity is the total displacement divided by the time interval during which the displacement occurred.
In SI, the unit of velocity is meters per second, abbreviated as m/s.

59. Chapter 2 Average Velocity Section 1 Displacement and Velocity
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60. Chapter 2 Velocity and Speed
Section 1 Displacement and Velocity
Chapter 2
Velocity and Speed
Velocity describes motion with both a direction and a numerical value (a magnitude).
Speed has no direction, only magnitude.
Average speed is equal to the total distance traveled divided by the time interval.

61. Interpreting Velocity Graphically
Section 1 Displacement and Velocity
Chapter 2
Interpreting Velocity Graphically
For any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph.
If the velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity.
Object 1: positive slope = positive velocity
Object 2: zero slope= zero velocity
Object 3: negative slope = negative velocity

62. Interpreting Velocity Graphically, continued
Section 1 Displacement and Velocity
Chapter 2
Interpreting Velocity Graphically, continued
The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path.
The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.

63. Sign Conventions for Velocity
Section 1 Displacement and Velocity
Chapter 2
Sign Conventions for Velocity
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