1. Introduction to Physics
Chapter 1

2. Introduction Physics is the most basic of the sciences
Deals with the behavior and structure of matter
Topics in Physics:
Motion, fluids, heat sound light, electricity and magnetism, relativity, atomic structure, condensed-matter physics, nuclear physics, elementary particles, and astrophysics.

3. 1-1 Science and Creativity
In general, the goal of all of the fields of science is to attempt to understand the world around us by exploring it in an orderly way.
Science is often times a creative activity
Example: observations and inferences
Aristotle ( B.C.) observed that objects given a push along the ground will slow to a stop → he inferred that the natural state of objects is to be at rest.
Galileo ( ) imagined that if friction was eliminated, an object put in motion would move indefinitely

4. 1-1 Science and Creativity
Theories are created to explain observations
Scientific theories can be viewed achievements, but they do require testing through experimentation to gain support
Theories are never absolutely verified – they are not “proved”
Theories can be modified or replaced as more is learned about natural phenomena
Copernicus’s Sun-centered theory of the universe vs. Ptolemy’s Earth-centered theory

5. 1-1 Science and Creativity
Theories are most valuable when they are simpler (or no more complex) than previous theories and unify and explain a greater variety of phenomena
These principles, in addition to quantitative agreement, influence the acceptance of a theory
Einstein’s theory of relativity differs very little from previous theories from Galileo and Newton in many situations – however, it has drastically altered our view of space-time and the relationship between mass and energy (E=mc ) 2

6. 1-2 Physics and Other Fields
It is not until the last couple of centuries that distinctions were made between different fields of science
The field of science that we consider as physics has been influenced by other fields (not just scientific fields) and continue to influence other fields.

7. 1-3 Models, Theories, and Laws
Model – a kind of analogy or mental image of the phenomena in terms of something we are familiar with
Models provide a mental or visual image when you cannot actually see what is happening
Examples: wave model of light; atomic models
Models vs. Theories

8. 1-3 Models, Theories, and Laws
Law – a concise but general statement about how nature behaves
Example: Law of Conservation Energy
Laws can sometimes take the form of a relationship or equation between quantities
Example: Newton’s equation F=ma

9. 1-3 Models, Theories, and Laws
Like theories, we can never be sure that laws are absolutely true – when new information is learned, laws can be modified or discarded
Theories – explain
Laws – describe (without explanation)

10. 1-4 Measurement and Uncertainty
In order to understand the natural world, scientists seek to find relationships between quantities
Examples: How does the magnitude of a force affect an object’s acceleration?
How does a change in temperature affect the pressure of a gas in a closed container?

11. 1-4 Measurement and Uncertainty
Accurate measurements are an important part of physics, but no measurement is absolutely precise
There is an uncertainty associated with every measurement
Uncertainty arises from various sources
Individual errors → Example: misusing equipment
The limited accuracy of every measuring instrument

12. 1-4 Measurement and Uncertainty
The number of reliably known digits in a number is called the number of significant figures
Significant figures in a measurement include all of the digits that are known precisely plus one last digit that is estimated
23.21 → 4 significant figures
0.062 → 2 significant figures

13. Significant Figures - Rules
1. Every nonzero digit in a recorded measurement is significant.
- Example: 24.7 m, m, and 714 m all have three sig. figs.
2. Zeros appearing between nonzero digits are significant.
- Example: 7003 m, m, and m all have 4 sig. figs.

14. Significant Figures - Rules
3. Zeros appearing in front of all nonzero digits are not significant; they act as placeholders and cannot arbitrarily be dropped (you can get rid of them by writing the number in scientific notation).
- Example: m has two sig. figs. And can be written as 7.1 x 10-3
4. Zeros at the end of the number and to the right of a decimal point are always significant.
- Example: m, m, and all have 4 sig. figs.

15. Significant Figures - Rules
5. Zeros at the end of a measurement and to the left of the decimal point are not significant unless they are measured values (then they are significant). Numbers can be written in scientific notation to remove ambiguity.
- Example: 7000 m has 1 sig. fig.; if those zeros were measured it could be written as x 103

16. Significant Figures - Rules
6. Measurements have an unlimited number of significant figures when they are counted or if they are exactly defined quantities.
- Example: 23 people or 60 minutes = 1 hour
* You must recognize exact values to round answers correctly in calculations involving measurements.

17. Significant Figures in Calculations
In calculations involving measurements, an answer cannot be more precise than the least precise measurement from which it was calculated.
Example: The area of a room that measures 7.7 m (2 sig. figs.) by 5.4 m (2 sig. figs.) is calculated to be m2 (4 sig. figs.) – you must round the answer to 42 m2

18. Significant Figures in Calculations
The answer to an addition or subtraction problem should be rounded to have the same number of decimal places as the measurement with the least number of decimal places.
Example: 34.61m – 17.3m = → 17.3 (1 decimal place)

19. Significant Figures in Calculations
In calculations involving multiplication and division, the answer is rounded off to the number of significant figures in the least precise term (least number of sig. figs.) in the calculations
Example: 8.3m x 2.22m = → 18m
Example: 8432m ÷ 12.5 = → 675m 2

20. Scientific Notation
scientific notation – a number is written as the product of two numbers: a coefficient and a power of ten
Example: 36,000 is written in scientific notation as 3.6 x 104 or 3.6e4
Coefficient = 3.6 → a number greater than or equal to 1 and less than 10.
Power of ten / exponent = 4
3.6 x 104 = 3.6 x 10 x 10 x 10 x 10 = 36,000

21. Scientific Notation
When writing numbers greater than ten in scientific notation the exponent is positive and equal to the number of places that the decimal has been moved to the left.

22. Scientific Notation
Numbers less than one have a negative exponent when written in scientific notation.
Example: is written in scientific notation as 8.1 x 10-3
8.1 x 10-3 = 8.1/(10 x 10 x 10) =
When writing a number less than one in scientific notation, the value of the exponent equals the number of places you move the decimal to the right.

23. Accuracy and Precision
Good measurements in the lab are both correct (accurate) and reproducible (precise)
accuracy – how close a single measurement comes to the actual dimension or true value of whatever is measured
precision – how close several measurements are to the same value

24. Accuracy and Precision
All measurements made with instruments are really approximations that depend on the quality of the instruments (accuracy) and the skill of the person doing the measurement (precision)
The precision of the instrument depends on the how small the scale is on the device.
The finer the scale the more precise the instrument.

25. SI Units
The International System of Units, SI, is a revised version of the metric system
Correct units along with numerical values are critical when communicating measurements.
The are seven base SI units (Table 1-2) of which other SI units are derived (derived units).
Sometimes non-SI units are preferred for convenience or practical reasons

26. Common SI Prefixes Units larger than the base unit Tera T Giga G
terameter (Tm)
Giga G
e-9 =
gigameter (Gm)
Mega M
e-6 =
megameter (Mm)
Kilo k
e-3 = 0.001
kilometer (km)
Hecto h
e-2 = 0.01
hectometer (hm)
Deka da
e-1 = 0.1
decameter (dam)
Base Unit
e0 = 1
meter (m)

27. Common SI Prefixes Units smaller than the base unit e0 = 1 Deci d
meter (m)
Deci d
e1 = 10
decimeter (dm)
Centi c
e2 = 100
centimeter (cm)
Milli m
e3 = 1000
millimeter (mm)
Micro μ
e6 = 1,000,000
micrometer (μm)
Nano n
e9 = 1,000,000,000
nanometer (nm)
Pico p
e12 = 1,000,000,000,000
picometer (pm)

28. Conversion Factors
The same quantity can usually be measured or expressed in many different ways.
Examples:
1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies
1 m = 10 dm = 100 cm = 1000 mm
Whenever two measurements are equal, a ratio of these measurements will equal one
Ratios of these equivalent (equal) measurements are called conversion factors.

29. Conversion Factors
In a conversion factor, the measurement in the numerator (on the top) is equivalent to the measurement in the denominator (on the bottom.
Example: “one meter per 100 centimeters”
Conversion factors are defined or exact quantities, which means they have an unlimited sig figs – your starting value determines your significant figures
1 m
100 cm

30. Conversion Factors
Because conversion factors are equal to one, when a measurement is multiplied by a conversion factor, the size of a measurement stays the same.
Example: How many meters are in 0.68 km?
1. Unknown: 0.68 km in meters
2. Known: km
- 1 km = 1000 m → Conversion Factor:
3/4. Solution-Calculation:
1000 m
1 km
0.68 km x m = m km

31. Dimensional Analysis
In dimensional analysis you use the units (dimensions) that are part of measurements to help solve (analyze) the problem
When using conversion factors in dimensional analysis always use the conversion factor that has the unit of the known in the denominator
This cancels the known unit and gives the answer in the unknown units

32. Displaying Data - Graphing
A well-designed graph can give you more information than either words, columns of numbers, or equations
However, for this to be true, the graph has to be drawn properly.

33. Displaying Data - Graphing
An important step in analyzing data is to identify the independent variable (or manipulated variable) and the dependent variables (or responding variables).
Independent variable – altered by the experimenter; influence other variables
Dependent variables – possibly change as a result of changes in the dependent variable.

34. Displaying Data - Graphing
See Table 2-2 an Figure 2-11 (handout)
What is the independent variable? What are the dependent variables?
What is the relationship between the independent variable and the dependent variables?

35. Linear Relationships m is the slope b is the y-intercept
When there is a linear relationship between two variables a graph of there relationship will be a straight line (see Figure 2-13).
This relationship can be written as a linear equation → y = mx + b
m is the slope
b is the y-intercept
Both are constants that can be found on the graph

36. Linear Relationships
Slope (m) – the ratio of vertical change (∆y) to horizontal change (∆x)
m = rise/run = ∆y / ∆x
To calculate slope choose two points, A and B, as far apart on the line as possible
∆y is equal to the difference in vertical values of A and B; ∆x is equal to the difference in horizontal values of A and B
Example (2-13): m = (20-0)m / (27-0)m/s
= 20m / 27m/s = 0.74s

37. Linear Relationships
y-intercept (b) – the point at which the line crosses the y-axis; it is the value of y when x is zero
Example (2-13): When x is zero, the value of y is zero → in cases like this, the equation becomes y = mx
If y gets smaller as x gets larger, then ∆y / ∆x is less than zero and the slope is negative
Example:

38. Quadratic Relationships
When a smooth line drawn through the data points curves upward (not a straight line), the graphs are frequently parabolas
This indicates that the variables are related by the equation: y = kx
This equation is one form of a quadratic relationship
k is a constant that shows you how fast y changes with x
See Figure 2-14 2 2

39. Inverse Relationships
Sometimes variables have an inverse relationship and form a hyperbola when graphed.
The general equation for an inverse relationship is xy = k or…
y = k(1/x) = kx -1

40. Manipulating Equations
The way in which quantities/variables relate to each other can be represented symbolically by an equation, as well as a graph.
Example: The relationship between the circumference of a circle and the circle’s diameter can be written as C = πd, or it can be represented as a linear graph
You can use the rules of algebra to rearrange equations
C = πd → d = C/ π

41. Solving Equations Using Algebra
From the graph of reaction distance versus speed → reaction distance = d; speed = v; and slope (which had units of time) = t
This relationship can be represented by the equation: d = vt or d = tv
d = tv has the same form, but different symbols then y = mx
You can solve for distance if you know the speed and time, but what if you know d and t and want to solve for v?

42. Solving Equations Using Algebra
When rearranging equations using algebra, any process that you do to one side of the equation you must do to the other side of the equation
Example: d = vt → Solve for v.
The steps can be performed in any sequence, but make sure you perform the same operations on both sides of the equation.

43. Solving Equations Using Algebra
Example: Solve the following equation for x. ay/x = cb/s
Example: Solve the following equation for x.
y = mx + b

44. Units in Equations
Most physical quantities have units and numerical values
When using quantities in equations you must substitute the numerical value and the units
Mathematical operations can be done on units just as they can be done on numbers
Make sure to use the same units for the same type of measurement
Example: If a problem involves length measurements in meters (m) and centimeters (cm) convert them both to the same units

45. Units in Equations Example: Solve for d using d = vt.
v = 11.0 m/s and t = 6.00 s