1. Chapter 1 Introduction
Ying Yi PhD
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2. What does Physics do? Develop Theory by experiment
Predict experiment results
More experiments Check prediction
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3. Outline Fundamental quantities & dimension analysis
Uncertainty in measurements (significant figures)
Coordinate system
Problem solving strategy
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4. Fundamental Quantities and Their Dimension
Length [L]
Mass [M]
Time [T]
Other physical quantities can be constructed from these three
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5. Units
To communicate the result of a measurement for a quantity, a unit must be defined
Defining units allows everyone to relate to the same fundamental amount
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6. Systems of Measurement
Standardized systems
Agreed upon by some authority, usually a governmental body
SI – Systéme International
Agreed to in 1960 by an international committee
Main system used in this text
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7. Length
Units
SI – meter, m
Defined in terms of a meter – the distance traveled by light in a vacuum during a given time
Also establishes the value for the speed of light in a vacuum
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9. Mass
Units
SI – kilogram, kg
Defined in terms of kilogram, based on a specific cylinder kept at the International Bureau of Weights and Measures
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11. Standard Kilogram
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12. Time
Units
seconds, s
Defined in terms of the oscillation of radiation from a cesium atom
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14. Other Systems of Measurements
cgs – Gaussian system
Named for the first letters of the units it uses for fundamental quantities
US Customary
Everyday units
Often uses weight, in pounds, instead of mass as a fundamental quantity
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15. Prefixes Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific abbreviation
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16. Structure of Matter Matter is made up of molecules
The smallest division that is identifiable as a substance
Molecules are made up of atoms
Correspond to elements
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17. More structure of matter
Atoms are made up of
Nucleus, very dense, contains
Protons, positively charged, “heavy”
Neutrons, no charge, about same mass as protons
Protons and neutrons are made up of quarks
Orbited by
Electrons, negatively charges, “light”
Fundamental particle, no structure
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18. Structure of Matter
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19. Dimensional Analysis Technique to check the correctness of an equation
Dimensions (length, mass, time, combinations) can be treated as algebraic quantities
Add, subtract, multiply, divide
Both sides of equation must have the same dimensions
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20. Example 1.1 Analysis of an equation
Show that the expression v=v0+at is dimensionally correct, where v and v0 represent velocities, a is acceleration, and t is a time interval.
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21. Example 1.2 Find an equation
Find a relationship between a constant acceleration a, speed v, and distance r from the origin for a particle traveling in a circle.
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22. Outline Fundamental quantities & dimension analysis
Uncertainty in measurements (significant figures)
Coordinate system
Problem solving strategy
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23. Uncertainty in Measurements
There is uncertainty in every measurement, this uncertainty carries over through the calculations
Need a technique to account for this uncertainty
We will use rules for significant figures to approximate the uncertainty in results of calculations
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24. Significant Figures A significant figure is a reliably known digit
All non-zero digits are significant
Zeros are significant when
Between other non-zero digits
After the decimal point and another significant figure
Can be clarified by using scientific notation
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25. Operations with Significant Figures
When multiplying and dividing, the number of significant figures in the final result is the same as the number of significant figures in the least accurate of the factors being combined
When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum
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26. Operations with Significant Figures, rounding
If the last digit to be dropped is less than 5, drop the digit
If the last digit dropped is greater than or equal to 5, raise the last retained digit by 1
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27. Example 1.3 Carpet Calculations
Several carpet installers make measurements for carpet installation in the different rooms of a restaurant reporting their measurements with inconsistent accuracy, as compiled in Table 1.6. compute the areas for (a) the banquet hall, (b) the meeting room, and (c) the dining room, taking into account significant figures. (d) what total area of carpet is required for these rooms?
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28. Conversion of units
When units are not consistent, you may need to convert to appropriate ones
See the inside of the front cover for an extensive list of conversion factors
Units can be treated like algebraic quantities that can “cancel” each other
Example:
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29. Examples 1.4 & 1.5
28.0 m/s= mi/h? 22.0 m/s2= km/min2
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30. Estimates Can yield useful approximate answers
An exact answer may be difficult or impossible
Mathematical reasons
Limited information available
Can serve as a partial check for exact calculations
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31. Order of Magnitude Approximation based on a number of assumptions
May need to modify assumptions if more precise results are needed
Order of magnitude is the power of 10 that applies
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32. Outline Fundamental quantities & dimension analysis
Uncertainty in measurements (significant figures)
Coordinate system
Problem solving strategy
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33. Coordinate Systems Used to describe the position of a point in space
Coordinate system consists of
A fixed reference point called the origin, O
Specified axes with scales and labels
Instructions on how to label a point relative to the origin and the axes
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34. Types of Coordinate Systems
Cartesian
Plane polar
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35. Cartesian coordinate system
Also called rectangular coordinate system
x- and y- axes
Points are labeled (x,y)
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36. Plane polar coordinate system
Origin and reference line are noted
Point is distance r from the origin in the direction of angle  from reference line
Points are labeled (r,)
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37. Trigonometry Review
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38. More Trigonometry Pythagorean Theorem
r2 = x2 + y2
To find an angle, you need the inverse trig function
For example, q = sin = 45.0°
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39. Degrees vs. Radians
Be sure your calculator is set for the appropriate angular units for the problem
For example:
tan = 30.00°
tan = rad
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40. Rectangular  Polar Rectangular to polar Polar to rectangular
Given x and y, use Pythagorean theorem to find r
Use x and y and the inverse tangent to find angle
Polar to rectangular
x = r cos 
y = r sin 
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41. Example 1.9 Cartesian and Polar Coordinates
(a) The Cartesian coordinates of a point in the xy-plane are (x, y)=(-3.50 m, m), as shown in Active Figure Find the polar coordinates of this point. (b) Convert (r, )=(5.00 m, 37.0o) to rectangular coordinates.
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42. Outline Fundamental quantities & dimension analysis
Uncertainty in measurements (significant figures)
Coordinate system
Problem solving strategy
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43. Problem Solving Strategy
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