1. Phy 131-Week 1 An Introduction

2. Part I
What is Physics?

3. SCIENCE is… The search for relationships that explain
and predict the behavior of the universe.

4. PHYSICS is… The science concerned with relationships between matter,
energy, and its
transformations.

5. Understanding Physics
Like all sciences, physics is based on experimental observations and quantitative measurements. 

6. Understanding Physics
Physics is a branch of science concerning study of natural phenomena, that is, properties of matter and energy.

7. Understanding Physics
Some examples of natural phenomena are
(a) sunrise and sunset,
(b) lightning and thunder,
(c) rainbow and blue sky,
(d) earthquake and tsunami.

8. Fields of study in Physics
In general, physics is concerned with the study of energy and the properties and structure of matter.
The fields of study in physics can be divided into classical physics and modern physics.
Classical physics deals with questions regarding motion and energy. It includes five important areas: mechanics (forces and motion), heat, sound, electricity and magnetism, and light.

9. Fields of study in Physics
Modern physics concentrates on scientific beliefs about the basic structure of the material world. Its major fields include atomic, molecular and electron physics, nuclear physics, particle physics, relativity, origin of the universe, and astrophysics.

10. Measurement and Base Quantities
Part II
Measurement and Base Quantities

11. Base Quantities
Physical quantities are quantities that can be measured.
A physical quantity can be represented by a symbol of the quantity, a numerical value for the magnitude of the quantity and the unit of measurement of the quantity.
Length, l = 1.67 m
l - symbol
m - unit
1.67is the value
Base quantities are physical quantities that cannot be defined in terms of other quantities.

12. Base Quantities Base quantities SI base units Name Symbol Length l
Name
Symbol
Length l
Metre m
Mass
Kilogram Kg
Time t
Second s
Electric current I
Ampere A
Temperature T
Kelvin K

13. Derived Quantities
Derived quantities are physical quantities derived from base quantities by multiplication or division or both. The unit for a derived quantity is known as a derived unit.

14. Derived Quantities Derived units Area = Length x breadth
[Area] = m x m = m2
Velocity =
[Velocity] = = ms–1
Acceleration=
Density =
[Density] = = kgm–3
[Acceleration] =
= ms–2

15. All measurements have some degree of uncertainty.
Precision
single measurement - exactness, definiteness
group of measurements - agreement, closeness together
Accuracy
closeness to the accepted value
accepted - observed
accepted
% error =
x 100%

16. An Example of the differences between precision and accuracy for a set of measurements:
Four student lab groups performed data collection activities in order to determine the resistance of some unknown resistor (you will do this later in the course). Data from 4 trials are displayed below.
Suppose the accepted value for the resistance is 500.
Then we would classify each groups’ trials as:
Group 1: neither precise nor accurate
Group 2: precise, but not accurate
Group 3: accurate, but not precise
Group 4: both precise and accurate
Group
Trial 1
Trial 2
Trial 3
Trial 4
Avg 1 34
612 78
126 2
127
128 3 20
500 62
980 4
502
501
503
498

17. Part III
Algebra for Physics

18. ALGEBRA & EQUATIONS
THE USE OF BASIC ALGEBRA REQUIRES ONLY A FEW FUNDAMENTAL RULES WHICH ARE USED OVER AND OVER TO REARRANGE AND SOLVE EQUATIONS.
(1) ANY NUMBER DIVIDED BY ITSELF IS EQUAL TO ONE.
(2) WHAT IS EVER DONE TO ONE SIDE OF AN EQUATION MUST BE DONE EQUALLY TO THE OTHER SIDE.
(3) ADDITIONS OR SUBTRACTIONS WHICH ARE ENCLOSED IN PARENTHESES ARE GENERALLY CARRIED OUT FIRST.
(4) WHEN VALUES IN PARENTHESES ARE MULTIPLIED OR DIVIDED BY A COMMON TERM EACH CAN BE MULTIPLIED OR DIVIDED SEPARATELY BEFORE ADDING OR SUBTRACTING THE GROUPED TERMS.

19. 10/10 =1 X /X = 1 Y /Y =1 10 + X + 5 = Y + 10 X + 15 = Y + 10 5 x (
ALGEBRA & EQUATIONS
RULE 1 – A VALUE DIVIDED BY ITSELF EQUALS 1
10/10 =1
X /X = 1
Y /Y =1
RULE 2 – OPERATE ON BOTH SIDES EQUALLY
10 +
X = Y
+ 10
X + 15 = Y + 10
IF WE ADD 10 TO THE
LEFT SIDE WE MUST
ADD 10 TO THE RIGHT
5 x (
X = Y )
5 x
X = Y
IF WE MULTIPLY THE LEFT
SIDE BY 5 WE MUST
MULTIPLY THE RIGHT BY 5
5X + 25 = 5Y

20. RULE 3 – OPERATION IN PARENTHESES ARE DONE FIRST
ALGEBRA & EQUATIONS
RULE 3 – OPERATION IN PARENTHESES ARE DONE FIRST
Y = ( ) ( X + 2)
Y = 9 ( X + 2 )
THE PARENTHESES
TERMS (5 + 5) ARE
ADDED FIRST
Y = 9 X + 18 2
S = T 2
S = T ( )
THE PARENTHESES
TERMS (22 – 7) ARE
SUBTRACTED FIRST
S = 225 T

21. Y = 4 ( T + 15 ) Y = 4 T + 60 Y = ( R x R ) - 3 R + 2 R - 6
ALGEBRA & EQUATIONS
RULE 4 – VALUES CAN BE DISTRIBUTED
THROUGH TERMS IN PARENTHESES
Y = 4 ( T + 15 )
Y = 4 T + 60
EACH TERM IN THE
PARENTHESES MUST
BE MULTIPLIED BY 4
Y =
( R x R )
- 3 R
+ 2 R
- 6
Y = ( R + 2 ) ( R - 3 )
Y = R R - 6 2
ALL TERMS MUST BE
MULTIPLIED BY
EACH OTHER THEN ADDED
Y = R R 2

22. SOLVING ALGEBRAIC EQUATIONS
SOLVING AN ALGEBRAIC EQUATION REQUIRES THAT THE UNKNOWN VARIABLE BE ISOLATED ON THE LEFT SIDE OF THE EQUAL SIGN IN THE NUMERATOR POSITION AND ALL OTHER TERMS BE PLACED ON THE RIGHT SIDE OF THE EQUAL SIGN.
THIS MOVEMENT OF TERMS FROM LEFT TO RIGHT AND FROM NUMERATOR TO DENOMINATION AND BACK, IS ACCOMPLISHED USING THE BASIC RULES OF ALGEBRA WHICH WERE PREVIOUSLY DISCUSSED.

23. SOLVING ALGEBRAIC EQUATIONS
THESE RULES CAN BE IMPLEMENTED PRACTICALLY USING SIMPLIFIED PROCEDURES (KEEP IN MIND THE REASON THAT THESE PROCEDURES WORK IS BECAUSE OF THE ALGEBRAIC RULES).
PROCEDURE 1 – WHEN A TERM WITH A PLUS OR MINUS
SIGN IS MOVED FROM ONE SIDE OF THE EQUATION
TO THE OTHER, THE SIGN IS CHANGED.
Y = 3X
- 5
N = 6 M
+ 4

24. SOLVING ALGEBRAIC EQUATIONS
PROCEDURE 2 – WHEN A TERM IS MOVED FROM
THE DENOMINATOR ACROSS AN EQUAL SIGN TO THE
OTHER SIDE OF THE EQUATION IT IS PLACED IN THE
NUMERATOR. LIKEWISE, WHEN A TERM IS MOVED
FROM NUMERATOR ON ONE SIDE IT IS PLACED IN THE
DENOMINATOR ON THE OTHER SIDE.
A C
B D =
----- = ---
F x K G
M N M B K =
F G x M
N x K
A C D =
x B

25. Trigonometry for Physics
Part IV
Trigonometry for Physics

26. TRIGNOMETRY
TRIGNOMETRIC RELATIONSHIPS ARE BASED ON THE RIGHT TRIANGLE (A TRIANGLE CONTAINING A 900 ANGLE). THE MOST FUNDAMENTAL CONCEPT IS THE PYTHAGOREAN THEOREM (A2 + B2 = C2) WHERE A AND B ARE THE SHORTER SIDES (THE LEGS) OF THE TRIANGLE AND C IS THE LONGEST SIDE CALLED THE HYPOTENUSE.
RATIOS OF THE SIDES OF THE RIGHT TRIANGLE ARE GIVEN NAMES SUCH AS SINE, COSINE AND TANGENT. DEPENDING ON THE ANGLE BETWEEN A LEG (ONE OF THE SHORTER SIDES) AND THE HYPOTENUSE (THE LONGEST SIDE), THE RATIO OF SIDES FOR A PARTICULAR ANGLE ALWAYS HAS THE SAME VALUE NO MATTER WHAT SIZE THE TRIANGLE.

27. The Right Triangle C = the hypotenuse A A & B = the legs B C A
900 
A & B
= the legs
Pythagorean Theorem
A B = C 2 B
C = A + B 2
A RIGHT TRIANGLE
A = C B 2  
900 +
= 1800
B = C A 2

28. TRIG FUNCTIONS
THE RATIO OF THE SIDE OPPOSITE THE ANGLE AND THE HYPOTENUSE IS CALLED THE SINE OF THE ANGLE. THE SINE OF 30 0 FOR EXAMPLE IS ALWAYS ½ NO MATTER HOW LARGE OR SMALL THE TRIANGLE. THIS MEANS THAT THE OPPOSITE SIDE IS ALWAYS HALF AS LONG AS THE HYPOTENUSE IF THE ANGLE IS (30 0 COORESPONSES TO 1/12 OF A CIRCLE OR ONE SLICE OF A 12 SLICE PIZZA!)
THE RATIO OF THE SIDE ADJACENT TO THE ANGLE AND THE HYPOTENUSE IS CALLED THE COSINE. THE COSINE OF 60 0 IS ALWAYS ½ WHICH MEANS THIS TIME THE ADJACENT SIDE IS HALF AS LONG AS THE HYPOTENUSE. (60 0 REPRESENTS 1/6 OF A COMPLETE CIRCLE, ONE SLICE OF A 6 SLICE PIZZA)
THE RATIO OF THE SIDE ADJACENT TO THE ANGLE AND THE SIDE OPPOSITE THE ANGLE IS CALLED THE TANGENT. IF THE ADJACENT AND THE OPPOSITE SIDES ARE EQUAL, THE RATIO (TANGENT VALUE) IS 1.0 AND THE ANGLE IS 45 0 ( 45 0 IS 1/8 OF A FULL CIRCLE)

29. Fundamental Trigonometry
(SIDE RATIOS)
Sin = A / C  C C C A A A
Cos = B / C  
Tan  = A / B B B B
A RIGHT TRIANGLE

30. The Use of Scientific Notation in Physics
Part V
The Use of Scientific Notation in Physics

31. Scientific Notation
Scientists have developed a shorter method of expressing very large or very small numbers. This method is called scientific notation or standard form.
Scientific notation is based on powers of the base number 10. The scientific notation in standard form is written as: 
A x 10n
Where:
(a) 1  A < 10 and A can be an integer or decimal number.
(b) n is a positive integer for a number greater than one or a negative integer for a number less than one.

32. Scientific Notation 450,000,000 = 450,000,000. x 10 8 2 3 1
RULE 1
As the decimal is moved to the left
The power of 10 increases one
value for each decimal place moved
Any number to the
Zero power = 1
450,000,000 = 450,000,000. x 10 8 2 3 1
450,000,000 = 450,000,000. x 10 8
4.5 x 10

33. Scientific Notation 0.0000072 = 0.0000072 x 10 -6 -2 -3 -1
RULE 2
As the decimal is moved to the right
The power of 10 decreases one
value for each decimal place moved
Any number to the
Zero power = 1
= x 10 -6 -2 -3 -1
= x 10 -6
7.2 x 10

34. When scientific numbers are multiplied
Scientific Notation
RULE 3
When scientific numbers are multiplied
The powers of 10 are added
100 x 1000 = 100,000 2
100 = 10
1000 = 10 3 2 3
(2 + 3) 5
x = = = 100,000 2 3 5
(3 x 10 ) x ( 2 x ) = 6 x 10

35. Scientific Notation 10000 / 100 = 100 4 10000 = 10 2 100 = 10 4 2
RULE 4
When scientific numbers are divided
The powers of 10 are subtracted
10000 / 100 = 100 4
10000 = 10 2
100 = 10 4 2
(4 - 2) 2
/ = = = 100 4 2 2
(5 x ) / (2 x ) = 2.5 x 10

36. Scientific Notation 2 (100) = 10,000 2 100 = 10 4 2 2 (2 x 2)
RULE 5
When scientific numbers are raised to powers
The powers of 10 are multiplied 2
(100) = 10,000 2
100 = 10 4 2 2
(2 x 2)
( ) = = = 10,000 2
(3000) = 9,000,000 3 2 2
(2 x 3) 6
(3 x ) = x = 9 x 10

37. Scientific Notation square root = 1/2 power cube root = 1/3 power 1/2
RULE 6
Roots of scientific numbers are treated as fractional
powers. The powers of 10 are multiplied
square root = 1/2 power
cube root = 1/3 power
1/2
10,000 = (10,000) 4
10,000 = 10
1/2
(1/2 x 4) 4
1/2
(10,000) = (10 ) = = 100
1/2
1/2 6
1/2 3 6
(9 x ) = x ( ) = x 10

38. Scientific Notation 2 2.34 x 10 3 + 4.24 x 10 --------- 3 2
RULE 7
When scientific numbers are added or subtracted
The powers of 10 must be the same for each term. 2
Powers of 10 are
Different. Values
Cannot be added !
2.34 x 10 3
x 10 3
Move the decimal
And change the power
Of 10 2
2.34 x = x 10 3
0.234 x 10
Power are now the
Same and values
Can be added. 3
x 10
4.47 x 10 3

39. Prefixes
Prefixes are used to simplify the description of physical quantities that are either very big or very small.

40. Prefixes Prefix Symbols Power/factor Value Giga- G 109 1 000 000 000
Mega- M
106
Kilo- k
103
1 000
Deci- d
10-1
0.1
Centi- c
10-2
0.01
Milli- m
10-3
0.001
Micro- μ
10-6
Nano- n
10-9

41. Unit Factors and Dimensional Analysis
Part VI
Unit Factors and Dimensional Analysis

42. Unit Conversion Using The Unit Factor Method
“Unit” Has Two Meanings:
“The” Unit (kg, s, m) or “Unit == ONE”
A Way To Convert Values From One Unit To Another
It Works Because If You Multiply Something Times 1 It Does Not Change The Value
Also called “Factor-Label” method

43. Unit Factors
Unit Factors Are Created From Conversion Factors Like 2.54 cm = 1 inch
We Can Make 2 Unit Factors From This

44. Using Unit Factors
Multiply The Value You Want To Convert By The Appropriate Unit Factor
Cancel Out Similar Units, Leaving The Desired Unit
Multiply Values and You Are Done!!
Example : How Many Inches Are In 25.4 Centimeters?

45. How Many Centimeters Are In Six Inches?
Using Unit Factors
In Your Notes
How Many Centimeters Are In Six Inches?

46. Using Unit Factors
In Your Notes
Express 24 cm in inches

47. Multiple Conversion Steps
You Can Also String Multiple Unit Factors Together
In Your Notes
How Many Seconds Are In 2 Years?

48. Dimensional Analysis
“Analyzing The Dimensions” Of An Equation To Be Sure The Units Match Up And Make Sense
Start With A Fancy, Schmanzy Equation
Replace Each Unknown With Its “Dimension”

49. Dimensional Analysis d = distance in meters = [m]
v = velocity in meters / second = [m]/[s]
a = acceleration in meters / second2 = [m]/[s]2
t = time in seconds = [s] or [s]2

50. Dimensional Analysis
[m] = [m]/[s] X [s] + ½ [m]/[s]2 X [s]2 Cancel Common Dimensions [m] = [m] + ½ [m] Ignore The ½ Factor [meters] = [meters] This Equation Is Dimensionally Consistent