Summarize the following text to main points and sub-points and make detailed explain for them:

e value inside the parentheses is equal to 1, since 1 inch is defined
as 2.54 cm.
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conversions
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conversions

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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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Using Order of Magnitude
Estimating too high for one number is oftencanceled by estimating too low for anothernumber
 The resulting order of magnitude is generallyreliable within about a factor of 10
 Working the problem allows you to dropdigits, make reasonable approximations andsimplify approximations
 With practice, your results will become betterand better

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Uncertainty in Measurements
There is uncertainty in every measurement –this uncertainty carries over through thecalculations
 May be due to the apparatus, the experimenter,and/or the number of measurements made
Need a technique to account for this uncertain
 We will use rules for significant figures toapproximate the uncertainty in results ofcalculations
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Significant Figures
A significant figure is one that is reliably known
 Zeros may or may not be significant
Those used to position the decimal point are not significant
To remove ambiguity, use scientific notation
 In a measurement, the significant figures include the first estimated digit.
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Significant Figures, examples
0.0075 m has 2 significant figures
 The leading zeros are placeholders only
 Can write in scientific notation to show more clearly:7.5 x 10-3 m for 2 significant figures10.0 m has 3 significant figures
The decimal point gives information about the reliability of the measurement
 1500 m is ambiguous
Use 1.5 x 103 m for 2 significant figures
Use 1.50 x 103 m for 3 significant figures
 Use 1.500 x 103 m for 4 significant figures
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Operations with SignificantFigures – Multiplying or Dividing
When multiplying or dividing, the number ofsignificant figures in the final answer is thesame as the number of significant figures inthe quantity having the lowest number ofsignificant figures.⚫ Example: 25.57 m x 2.45 m = 62.6 m2⚫ The 2.45 m limits your result to 3 significantfigures
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Operations with SignificantFigures – Adding or Subtracting
When adding or subtracting, the number ofdecimal places in the result should equal thesmallest number of decimal places in anyterm in the sum.⚫ Example: 135 cm + 3.25 cm = 138 cm⚫ The 135 cm limits your answer to the unitsdecimal value
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Operations With SignificantFigures – Summary
The rule for addition and subtraction are different than the rule for multiplication and division⚫ For adding and subtracting, the number of decimal places is the important consideration⚫ For multiplying and dividing, the number ofsignificant figures is the important consideration
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Rounding
Last retained digit is increased by 1 if the last digitdropped is greater than 5⚫ Last retained digit remains as it is if the last digit dropped is less than 5⚫ If the last digit dropped is equal to 5, the retained digit should be rounded to the nearest even number⚫ Saving rounding until the final result will helpeliminate accumulation of errors
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Basic Quantities and Their Dimension
Dimension has a specific meaning – it denotes the physical nature of a quantity.
Dimensions are often denoted with square brackets.
 Length [L]
 Mass [M]
 Time [T]
Dimensions and Units
Each dimension can have many actual units.
Table 1.5 for the dimensions and units of some derived quantities
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Dimensions and Units

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Dimensional Analysis
Technique to check the correctness of an equation or to assist in deriving 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.
Any relationship can be correct only if the dimensions on both sides of the equation
are the same.
Cannot give numerical factors: this is its limitation
Example: Given the equation:
x = ½ at 2  Check dimensions on each side:





The T2’s cancel, leaving L for the dimensions of each side.
The equation is dimensionally correct.
There are no dimensions for the constant.
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Dimensional Analysis to Determine a Power Law
Determine powers in a proportionality
 Example: find the exponents in the expression
        

You must have lengths on both sides.
 Acceleration has dimensions of L/T2
 Time has dimensions of T.
 Analysis gives
Example
Suppose that the acceleration of a particle moving in circle of radius r with uniform velocity v is proportional to the rn  and v m. Use the dimensional analysis to determine the power n and m.
Solution
Let us assume
a is represented in this expression a =
Where k is the proportionality constant of dimensionless unit.
The right hand side

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The left hand side


Therefore

Hence

n+m=1 and m=2
Therefore. n =-1 and the acceleration a is
k=1
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Models of Matter
Some Greeks thought matter is made of atoms.
No additional structure
JJ Thomson (1897) found electrons and showed
atoms had structure.
Rutherford (1911) determined a central nucleus
surrounded by electrons.
Nucleus has structure, containing protons and
neutrons
Number of protons gives atomic number
Number of protons and neutrons gives mass
number
Protons and neutrons are made up of quarks.
Six Quarks: Up, down, strange, charmed, bottom, top
Fractional electric charges
 +⅔ of Up, charmed, top
 ⅓ of Down, strange, bottom
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Summary :