math of physics
TRANSCRIPT
“God chose to make the universe according to
very beautiful mathematics.”
Paul Dirac
Mathematics of
Physics
Mathematics of Physics• The first step in the scientific study of any phenomenon is to quantify it.•Describe it fully in terms of numerical measurements
Mathematics of Physics•Quantities• Systems of Measurement• Conversions• Significant Figures
• Scientific Notation• Literal Equations
• Physical Quantity is a number that is used to describe a physical phenomenon• For each physical quantity there are generally accepted units of measurement
Quantities
2 Kinds of Units of Measurement• Fundamental Units – basic units•Derived Units – combination of two or more fundamental units
Quantities
• International System (SI) MKS CGS• FPS System ( English System)
Systems of Units
Meter, Kilogram, SecondCentimeter, gram, Second
Foot, Pound, Second
Systems of UnitsFUNDAMENTAL PHYSICAL QUANTITIES
IN SI UNITSQUANTITY UNIT symbolLENGTH Meter m
mass Kilogram kg
time Second s
Electric Current Ampere A
Temperature Kelvin K
Amount of Substance
Mole mol
Luminous Intensity
Candela cd
• Unlike quantities cannot be added or subtracted.
Systems of Units
Examples:1 meter + 2 seconds6 grams – 3 Kelvin2 Newtons + 5 Newtons
Not possible
Not possible
possible
• Before like quantities can be added or subtracted, they must be expressed in the same unit; this is also the unit in which the sum or difference is expressed.
Systems of Units
Systems of UnitsExample:1 kiloMeter + 300 Meters1000 Meters + 300 MetersAnswer: 1300 meters1 kiloMeter + 0.3 kiloMeterAnswer: 1.3 kiloMeters
possible
Systems of Units• Any quantities can be multiplied or divided. Their units must also be multiplied or divided to obtain the unit in which the result is expressed.Examples:(1 kiloMeter) (300 seconds) 6 grams / 3 Kelvinpossible
possible
Systems of UnitsExamples: (1 kiloMeter) (300 seconds) Answer: 300 (kilometer)(second) 6 grams / 3 KelvinAnswer: 2 grams / Kelvin
• Before like quantities are multiplied or divided, they must be expressed in the same unit.
Systems of Units
Example:(1 kiloMeter) (300 Meters)(1000 Meters) (300 Meters)
Answer: 300,000 meter2
(1 kiloMeter) (0.3 kiloMeter)
Answer: 0.3 kiloMeter2
Systems of Units
Answer:
ExercisesPage 24Notebook
Metric-Metric Conversion• Look at the Table of Prefixes• Determine the power of ten corresponding to each unit
Conversion
Example: Change 0.14 mg to kg
millikilo
• If the new power of ten is higher, move the decimal point to the left; If it is Lower, move the decimal point to the Right.• The difference between the powers of ten tells you how many places to move the decimal point.
Conversion
ConversionExample: Change 0.14 mg to kg
milli kilo- 3 + 3
Greater by 6
Move decimal point 6 places to the leftAnswer: 0.14 mg = 0.00000014 kg
ConversionExample: Change 53.6 Ms to hs
Mega
hecto
less by 4
Move decimal point 4 places to the Right
Answer: 53.6 Ms = 536000 hs
+ 6 + 2
Answer:
Exercises (left side)Page 25Notebook
ConversionOther Conversions• Select a conversion factor so that canceling removes the undesired unit and leaves the desired unit.Example: Change 46.5 ft to m
undesired
desiredConversion
factor: 1 m = 3.281 ft
Conversion•Write the conversion factor like this:
(46.5 ft) (1m)
(3.281 ft)14.2 m
• Cancel out the units• Perform the operation and copy the remaining unit
Conversion• Chain several conversionsHow many seconds are there in 4 days?(4 days) (24 hr) (60 min) (60 s)
(1 day) (1 hr) (1 min)Answer: 345,600 s
• Complex conversionsConvert 60 mi/hr to m/s
Conversion Factors: 1 mi = 5280 ft 1 hr = 60 min
1 m = 3.281 ft 1 min = 60 s
Conversion
(60 mi) (5280 ft) (1 m) (1 hr)
(hr) (1 mi) (3.281 ft) (3600 s)
Answer: 27 m/s
Conversion
Answer:
Exercises (Right side)Page 25Notebook