“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