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CHAPTER 1PHYSICAL QUANTITIES AND UNITS1Base Quantities and Derived Quantities

PHYSICAL QUANTITIES

Base Quantities

Physical quantities are quantities that can be measured.

Base Quantities

A physical quantity can be represented by a symbol of the quantity, a numerical value for the magnitude of the quantity and the unit of measurement of the quantity. Length, l = 1.67 ml - symbol1.67is the valuem - unit

Base Quantities

Base quantities are physical quantities that cannot be defined in terms of other quantities.Base quantity :LengthDerived quantity :Area = length x length6UnitsSI (Systme Internationale) Units:mks: L = meters (m), M = kilograms (kg), T = seconds (s)cgs: L = centimeters (cm), M = grams (g), T = seconds (s)

British Units:Inches, feet, miles, pounds, slugs...

We will switch back and forth in stating problems.

Base Quantities and Units

Table shows common base quantities and their respective SI units.QuantityDimensionUnit (SI)SymbolLengthLmetermMassMkilogramkgTimeTsecondSElectric CurrentIAmpereATemperature kelvinKAmount of substance-molemolLuminous intensity-candelacdDerived QuantitiesDerived quantities are physical quantities derived from base quantities by multiplication or division or both. The unit for a derived quantity is known as a derived unit.Table 1.2 shows some examples of derived quantities and their corresponding derived units. Several derived units are complex. Special names are substituted for these units. For example, the unit for the derived quantity, force, is the newton (N).

Derived Quantities & Units

Some SI derived unitsQuantityDimensionsSI unitsCommon nameArealength lengthm2square meterVelocitylength/timem/sDensitymass/volumekg/m3Frequencycycles/times-1hertz (Hz)Accelerationvelocity/timem/s2Forcemass accelerationkg m/s2Newton (N)Work, Energy, Heatforce distancekg m2/s2Joule (J)Pressure Force / Areakg m-1s-2

Pascal (Nm-2)10Unit Dimensions11Fundamental Units- DimentionsLength [L]FootMeter - Accepted UnitFurlongTime [T]Second - Accepted UnitMinuteHourCenturyMass [M]Kilogram - Accepted UnitSlug12Derived UnitsSingle Fundamental UnitArea = Length Length [L]2Volume = Length Length Length [L]3

Combination of UnitsVelocity = Length / Time [L/T]Acceleration = Length / (Time Time) [L/T2]Jerk = Length / (Time Time Time) [L/T3]Force = Mass Length / (Time Time) [M L/T2]13Unit ConversionUseful Conversion Factors:1 inch= 2.54 cm1 m = 3.28 ft1 mile= 5280 ft 1 mile = 1.61 km

Example: convert miles per hour to meters per second:

14Orders of MagnitudePhysical quantities span an immense range

Lengthsize of nucleus ~ 10-15 msize of universe ~ 1030 m

Timenuclear vibration ~ 10-20 sage of universe ~ 1018 s

Masselectron ~ 10-30 kguniverse ~ 1028 kg

15Physical ScaleOrders of Magnitude Set the ScaleAtomic Physics ~ 10-10 mBasketball ~ 10 mPlanetary Motion ~ 1010 mKnowing the scale lets us guess the ResultQ: What is the speed of a 747?Distance - New York to LA 4000 miFlying Time 6 hrs= 660 mph16Dimensional AnalysisFundamental QuantitiesLength - [L]Time - [T]Mass - [M]

Derived QuantitiesVelocity - [L]/[T]Density - [M]/[L]3 Energy - [M][L]2/[T]2

17Physical QuantitiesMust always have dimensionsCan only compare quantities with the same dimensionsv = v(0) + a t[L]/[T] = [L]/[T] + [L]/[T]2 [T]

Comparing quantities with different dimensions is nonsensev = a t2[L]/[T] = [L]/[T]2 [T]2 = [L]

Scientific Notation1 Scientists have developed a shorter method of expressing very large or very small numbers. This method is called scientific notation or standard form.Distance from house to school : 5 000 mScientific Notation2Scientific notation is based on powers of the base number 10. The scientific notation in standard form is written as:A x 10nwhere(a)1 A < 10 and A can be an integer or decimal number.(b)n is a positive integer for a number greater than one or a negative integer for a number less than one.

PrefixesPrefixes are used to simplify the description of physical quantities that are either very big or very small.It is not easy to figure out a distance of 100 000 mm. Neither it is easy to imagine the size of an atom which has a radius of 0.0000005 m.

Prefixes are the preceding factor used to represent very small and very large physical quantities in SI units.

Prefixes