1. * INTRODUCTION Physical quantities Base quantities Derived quantities Prefixes Scientific notation (standard form Scalar quantities Vector quantities Dimensional Analysis CONCEPTUAL MAP

2. PHYSICAL QUANTITIES A quantity that can be measured. A physical quantities have numerical value and unit of measurement. For example temperature 30 degrees celcius, 30 is numerical value & ‘degree celcius’ is the unit. Written as 30 o C. * Temperature = 30 degree Celcius = 30 o c Physical quantity = numerical value x unit measurement

3. 1.A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit. 2.The physical quantities can be classified into base quantities and derived quantities. 3.There are seven base quantities: length, mass, time, current, temperature, amount of substance and luminous intensity. 4.The SI units for length, mass and time are metre, kilogram and second respectively. 5.Prefixes are used to denote very big or very small numbers.

4. BASE QUANTITIES Base Quantities are physical quantities that cannot be derived from other physical quantities. Scientific measurement using SI units (International System Units). Base Quantities SymbolSI UnitSymbol of SI unit LengthLmeterm Massmkilogramkg Timetseconds TemperatureTKelvinK Electric currentIampereA Table 1.1 Shows five base quantities and their respective SI units

5. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 Vector quantities are quantities that have both magnitude and direction Magnitude = 100 N Direction = Left A Force Scalars and Vectors

6. Physical Quantities, Units and Measurement T H E M E O N E : M E A S U R E M E N T C h a p t e r 1 Scalar quantities are quantities that have magnitude only. Two examples are shown below: Measuring Mass Measuring Temperature

7. 7 Mass: The amount of matter in a body. SI Units: kilogram (kg) Common Units: pounds (lbs) and ounces (oz) 1 kg is approx. 2.2 lbs 1 kg = 1000 g 1 oz = 28.35 g This Platinum Iridium cylinder is the standard kilogram.

8. 8 Length: A measure of distance. SI Unit: meter (m) Common Units: inches (in); miles (mi) 1 in = 2.54 cm = 0.0254 m 1 mi = 1.609 km = 1609 m

9. 9 Volume: Amount of space occupied by a body. SI Unit: cubic meter (m 3 ) Common Units: Liter (L) or milliliter (mL) or cubic centimeter (cm 3 )

10. 10 Density: Amount of mass per unit volume of a substance. SI Units: kg/m 3 Common Units: g/cm 3 or g/mL

11. International system SI Unit (m K s) International system (c g s) Unit International system (f b s) Unit Measuring Systems

12. 1.2 SI Units Example of derived quantity: area Defining equation:area = length × width In terms of units:Units of area = m × m = m 2 Defining equation:volume = length × width × height In terms of units:Units of volume = m × m × m = m 3 Defining equation: density = mass ÷ volume In terms of units:Units of density = kg / m 3 = kg m −3 L W H L W

13. 1.2 SI Units Work out the derived quantities for: Defining equation:velocity = In terms of units:Units of speed = m/s Defining equation:acceleration = In terms of units:Units of acceleration = m/s 2 Defining equation: force = mass × acceleration In terms of units:Units of force = Kg m/s 2

14. Defining equation: Work = Force x Displacement In terms of units:Units of Work = J = Kg m 2 /s 2 1.2 SI Units Defining equation: Energy = Mass x gravity x high In terms of units:Units of Energy = J = Kg m 2 /s 2 Defining equation: Power = Force x displacement / time Defining equation: Pressure = Force / area In terms of units:Units of Power = W = Kg m 2 /s 3 In terms of units:Units of Pressure = Kg m /m 2 s 2 = Kg m -1 /s 2 = N/m 2

15. DERIVED QUANTITIIES Derived Quantities are physical quantities derived from combination of base quantities through multiplication or division or both Derived QuantitiesSymbolRelationship with base quantitiesDerived units AreaALength x Lengthm2m2 VolumeVLength x Length x Lengthm3m3 DensityρMass Length x Length x Length kg/m 3 VelocityvDisplacement Time m/s AccelerationaVelocity Time m/s 2 ForceFMass x AccelerationN WorkWForce x DisplacementJ EnergyEpEkEpEk Mass x gravity x high = ½ x mass x velocity x velocity J PowerPForce x Displacement Time W PressurepForce Area N/m 2 Table 1.2 shows some of the derived quantities and their respective derived units

16. 16 Temperature: is the measure of how hot or cold an object is. SI Unit: Kelvin (K) Common Units: Celsius (ºC) or Fahrenheit (ºF) Converting between K, ºC and ºF: T K = T C +273.15 T C = T K – 273.15 T F = 9/5 T C + 32 T C = 5/9 (T F – 32)

18. “When the thermometer is held in the mouth or under the armpit of a living man in good health” it indicates 98 F Black board example 19.1 a)What is the temperature in Celsius (centigrade)? b)What is the temperature in Kelvin?

19. PREFIXES Prefixes : are used to simplify the description of physical quantities that are either very big or very small. PrefixSymbo l Value PetaP10 15 teraT10 12 gigaG10 9 megaM10 6 kilok10 3 hektoh10 2 dekada10 decid10 -1 centic10 -2 millim10 -3 micro  10 -6 nanon10 -9 picoP10 -12 FemtoF10 -15 Table 1.4 Lists some commonly used SI prefixes

20. * STANDARD FORM Standard form or scientific notation is used to express magnitude in a simpler way. In scientific notation, a numerical magnitude can be written as : A x 10 n, where 1 ≤ A < 10 and n is an integer Example 1.1 : For each of the following, express the magnitude using a scientific notation. I.The mean radius of the balloon = 100 mm II.The mass of a butterfly = 0.0004 kg Solution: The mean radius of the balloon = 100 mm =100 x 10 -3 m = 0.1 m The mass of a butterfly = 0.0004 kg =0. 0004 x 10 3 g = 0.4 g

21. Dimensional Analysis The word dimension in physics indicates the physical nature of the quantity. For example the distance has a dimension of length, and the speed has a dimension of length/time. The dimensional analysis is used to check the formula, since the dimension of the left hand side and the right hand side of the formula must be the same.

22. Example Using the dimensional analysis check that this equation x = ½ at 2 is correct, where x is the distance, a is the acceleration and t is the time. Solution x = ½ at 2 This equation is correct because the dimension of the left and right side of the equation have the same dimensions.

23. Example Show that the expression v = v o + at is dimensionally correct, where v and v o are the velocities and a is the acceleration, and t is the time Solution The right hand side [v] = L/T The left hand side L/T + L/T Therefore, the expression is dimensionally correct.

24. Example Suppose that the acceleration of a particle moving in circle of radius r with uniform velocity v is proportional to the r n 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 = k r n v m Where k is the proportionality constant of dimensionless unit. The right hand side n+m=1 and m=2 Therefore. n =-1 and the acceleration a is a = k r -1 v 2 k = 1 a= v 2 /r

25. Exercise Part A: See if you can determine the dimensions of the following quantities: volume acceleration (velocity/time) density (mass/volume) force (mass × acceleration) charge (current × time) Check your answers You are correct if you wrote down: 1.Volume L 3 2.acceleration (velocity/time) L/T 2 3.density (mass/volume) M/L 3 4.force (mass × acceleration) M·L/T 2 5.charge (current × time) I·T

26. Check your answers 1. pressure (force/area)M·L -1 ·T -2 2. (volume) 2 L6L6 3. electric field (force/charge)M·L·I -1 ·T -3 4. work (in 1-D, force × distance)M·L 2 /T 2 5. energy (e.g., gravitational potential energy = mgh = mass × gravitational acceleration × height) M·L 2 /T 2 6. square root of areaL Part B: Now find the dimensions of these: 1.pressure (force/area) 2.(volume) 2 3.electric field (force/charge) 4.work (in 1-D, force × distance) 5.energy (e.g., gravitational potential energy = mgh 6.square root of area

27. Which one of the following quantities are dimensionless? 1-68 2-sin (68 ) 3-e 4-force 5-6 6-frequency 7-log (0.0034)

28. What are the dimensions of the following? 1.[sin (  t)] 2.[3] 3.[force] 4.[height] 5.[frequency] 6.[displacement] 7.[area × volume] 8.[0.5 × volume]