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Topic 1 Physical quantities and units Physics and Physical Measurement

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LEARNING OUTCOMES (a) show an understanding that all physical quantities consist of a numerical magnitude and a unit (b) recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol) (c) express derived units as products or quotients of the base units and use the named units listed in this syllabus as appropriate (d) use base units to check the homogeneity of physical equations (f) use the following prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: pico (p), nano (n), micro ( ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T) (g) make reasonable estimates of physical quantities included within the syllabus

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FOR YOUR NOTES All physical quantities have a magnitude and a unit Base units are: mass (kg) length(m) time (s) current (A) temperature (K) amount of substance (mol) Express derived units in terms of the base units Use the SI units

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Standards of Measurement SI units are those of the Systme International dUnits adopted in 1960 Used for general measurement in most countries Scientists and engineers need to make accurate measurements so that they can exchange information To be useful a standard of measurement must be Invariant, Accessible and Reproducible

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Fundamental dimensions There are seven fundamental dimensions. A base unit is accurately defined for each quantity. They are: Lengthmetrem Masskilogram kg Timeseconds Electric currentampereA Thermodynamic tempKelvinK Amount of a substancemolemol Luminous intensitycandela Cd

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Derived Quantities Speed, force, energy etc. are not base quantities. Derived units allow us to measure any quantity. Derived quantities are combinations of the fundamentals e.g. speed average speed = distance/time So the derived unit is meters per second We write derived units in the form ms -1 not m/s

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Figuring out derived units Write out an equation for the quantity you want to know the units of. ( The defining equation is best) eg Pressure = F/A Rewrite the equation substituting units for quantities Eg [Pa]=[N] / [m 2 ] or [N] [m -2 ] Check if units are base units m -2 Repeat process for any none base units F=ma [N] = [kg] [m] [s -2 ]all base units So.. [Pa]= [N] [m -2 ] = [kg] [m] [s -2 ] [m -2 ] Simplified [Pa]= [kg] [s -2 ] [m -1 ]

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Practise Try these Velocity Density Work Power Resistance

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Writing Units two examples A car has a velocity of 10ms -1 Notes 1. Do not use m/s 2. Meters and seconds are SI units A metal has a density of 5Kgm -3 Notes 1. Kg not g is the SI unit 2. Per m3 is written m -3

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Some Derived Units Acceleration ms -2 Angular acceleration rad s -2 Momentumkgms -1 or Ns Others have specific names and symbols Force kg ms -2 or N Pressurekgm -1 s -2 or Pa Resistancekgm 2 A -2 s -3 or Of course there are so many things out there to measure there are many more.

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Summary questions What are the base quantities? What are the base units? Give 5 derived units What is a volume of 1m 3 in cm 3 ? What is a pressure of 1Ncm -2 in Pa? State 2 problems with this reading and rewrite it correctly: Speed= 39 mph

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Can you? State the fundamental units in the SI system. Distinguish between fundamental and derived units Give examples of derived units. Convert between different units of quantities. State units in the accepted SI format.