1. INTRODUCTION AND MATHEMATICAL CONCEPTS
CHAPTER 1
INTRODUCTION AND MATHEMATICAL CONCEPTS

2. 1.1 The Nature of Physics Laws of physics: Galileo and Newton
Describe heat generated by burning match
Determine star speed
Assist police with radar
Galileo and Newton
Laws have roots in rocketry and space travel

3. 1.1 The Nature of Physics Physics is the core of: X-rays
Telecommunication
Lasers
Electronics

4. 1.2 Units SI CGS BE Length Meter (m) Centimeter(cm) Foot (ft) Mass
System SI
CGS BE
Length
Meter (m)
Centimeter(cm)
Foot (ft)
Mass
Kilogram (kg)
Gram (g)
Slug (sl)
Time
Second (s)

5. 1.2 Units
Base Units used with laws to define additional units for quantities
Force
Energy
Derived Units combinations of base units

6. 1.3 The Role of Units in Problem Solving
Conversion of Units
3.281 ft = 1 m
Ex. 1
Express 979 m in ft
979 m ft = ft
1 m

7. 1.3 The Role of Units in Problem Solving
If units do not combine algebraically to give desired results  conversion is not correct
Ex. 2 Express 65 mi/hr in m/s
65 mi 5280 ft hr m meter
1 hr 1 mi s ft sec
 Only quantities with same units can be added or subtracted

8. 1.3 The Role of Units in Problem Solving
Dimensional Analysis
Dimension= physical nature of a quantity and type of unit used to specify it
Ex: Distance Length {L}
used to check validity of equation

9. 1.4 Trigonometry
sinØ= ho/h
cosØ= ha/h
tanØ= ho/ha h ho ø ha

10. 1.4 Trigonometry Ex: Trig ho ha= 67.2 m ho= ?? tanØ= ho/ha
ho= (ha)(tanØ) = (67.2m)(tan50°) = 80m ho
50°
ha= 67.2 m

11. 1.4 Trigonometry Inverse Functions
used to find angle if two sides are known
Ø= Sin-1(ho/h)
Ø=Cos-1(ha/h)
Ø=Tan-1(ho/ha)

12. 1.4 Trigonometry Pythagorean Theorem
Square length of hypotenuse of Right Triangle is equal to sum of square of lengths of other two sides
h2= ho2 + ha2

13. 1.5 The Nature of Physical Quantities: Scalars & Vectors
Scalar Quantity
One that can be described by a single number (including units) giving its size or magnitude
Answers “How much is there?”
Ex: Volume, Time, Temperature, Mass

14. 1.5 The Nature of Physical Quantities: Scalars & Vectors
Vector Quantity
One that deals inherently with both magnitude and direction
Arrows used to show direction
Direction of arrow = Direction of vector
Length of arrow is proportional to magnitude
All forces are vectors
Force = push/pull
Magnitude measured in Newtons

15. 1.5 The Nature of Physical Quantities: Scalars & Vectors
Main Difference
Scalars do not have direction; vectors do
Negative and positive signs do not always indicate a vector quantity
Vector has physical direction (east, west)
Temperatures have (+) and (-) , but no direction  not a vector

16. 1.6 Vector Addition & Subtraction
When adding vectors you must take both magnitude and direction into account

17. 1.6 Vector Addition & Subtraction
Colinear
2 or more vectors that point in the same direction
Arrange head-to-tail and add length of total displacement  Gives the resultant vector
R = A + B
Only works with this type of vector addition A B R

18. 1.6 Vector Addition & Subtraction
Perpendicular
2 vectors with a 90° angle between them
Arrange head to tail and use pythagorean theorem
R2 = A2 + B2 R A B

19. 1.6 Vector Addition & Subtraction
Not colinear, not perpendicular
Must add graphically
Draw the components head-to-tail proportionally & accurately
Measure the resultant

20. 1.6 Vector Addition & Subtraction
Multiply one of the vectors by –1 to reverse direction
Add like before

21. 1.7 The Components of a Vector
Vector Components
Components of vector can be used in place of the vector itself in any calculation in which it is convenient to do so
Components are any two vectors that add up vectorally to the original vector
R= x + y R y x

22. 1.7 The Components of a Vector
In two dimensions the vector components of a vector A are two perpendicular vectors Ax and Ay that are parallel to the x & y axes
Add together so that A = Ax + Ay
Do not have to be x & y, but it is easier to use them ( especially with trig )

23. 1.7 The Components of a Vector
For a vector to be zero, all its components must be zero
Two vectors are equal if, and only if, they have the same magnitude and direction
If they are equal, their components are equal

24. 1.8 Addition of Vectors by Means of Components
Components are most convenient and accurate way to add vectors
If C= A + B
Then Cx = Ax + Bx and Cy= Ay + By By C Bx Ay Ax

25. 1.8 Addition of Vectors by Means of Components
Example: A jogger runs 145 m in a direction of 20.0° east of north (displacement vector A) and then 105 m in a direction 35.0° south of east (displacement vector B). Determine the magnitude and direction of the resultant vector C for these two displacments

26. 1.8 Addition of Vectors by Means of Components
Vector x Component y Component
A Ax=(145m)(sin20.0°) Ay= (145m)(coz20.0°)
=49.6m =136m
B Bx=(105m)(cos35.0°) By= -(105m)(sin35.0°)
=86.0m = -60.2m
C Ax + Bx = Cx = m Ay + By = Cy = 76 m

27. 1.8 Addition of Vectors by Means of ComponentsBx Ax
35.0°
B= 105 m Ay
A= 145 m By
20.0° C

28. 1.8 Addition of Vectors by Means of Components
C²= Cx² + Cy² = 155m
Ø=Tan-1(76m/135.7m) = 29°

29. Vocabulary
Base SI units- units for length (m), mass (kg), and time (s).
Derived units- units that are combinations of the base units.
Trigonometry-
Sinθ = ho/h Cosθ = ha/h Tanθ = ho/ha

30. Vocabulary Pythagorean Theorem- h^2=ho^2+ha^2
Scalar quantity- A single number giving its size or magnitude.
Vector quantity- A quantity that deals inherently with both magnitude and direction.
Resultant vector- the total of the vectors.
Vector components- two perpendicular vectors Ax and Ay that are parallel to the x and y axes, respectively, and add together vectorially so that A=Ax+Ay.

31. Mathematical Steps
Draw vectors (sketch)
Add Graphically (for estimation)
Make a chart
Find Components (Horizontal and Vertical)
Check your signs
Add columns of the chart together
Draw the resulting components
Draw the resultant
Use Trig and the Pythagorean Theorem to get angle and total length