Physics 2 (PHY 125) Classical Mechanics Dr Manjunatha S

PHYSICAL QUANTITY: A quantity which can be measured directly or indirectly is called physical quantity Measurement means comparison of physical quantity with another standard. UNIT In order to measure a physical quantity, a standard reference is needed. This standard is called unit. Physical Quantity = number x unit 2Dr Manjunatha S

Measurement Being quantitative in Physics requires measurements How tall is Ming Yao? How about his weight? –Height: 2.29 m (7 ft 6 in) –Weight: 141 kg (310 lb) Number + Unit –“thickness is 10.” has no physical meaning –Both numbers and units necessary for any meaningful physical quantities

Units Two types of Units 1.Fundamental Units: In mechanics, the mass, length, and time are fundamental physical quantities. The units of these physical quantities are called fundamental units. 2. Derived Units: Any physical quantity which can be derived from the fundamental physical quantities is called derived units. 4Dr Manjunatha S

System of units: A complete set of fundamental and derived units is known as system of units. There are four system of units. 1.CGS system: The unit of length is centimetre (cm), mass is gram (g)and time is second (s). 2. FPS system: foot, pound and second 5Dr Manjunatha S

System of units: 3. MKS System: meter, Kilogram and second. 4. SI units (System of International Units): Modified MKS system, consists of 7 fundamental units, 2 supplementary units and many derived units. 6Dr Manjunatha S

Fundamental Quantities and SI Units 1. Length meter m 2. Masskilogramkg 3. Timeseconds 4. Electric CurrentampereA 5. Thermodynamic Temperature KelvinK 6. Luminous Intensitycandelacd 7. Amount of Substance molemol 7Dr Manjunatha S

Supplementary Units S. NoPhysical QuantityName of unitsymbol 1Plane Angleradian rad 2Solid AnglesteradianSr 8Dr Manjunatha S

Derived Units S. No. Physical QuantityName of UnitSymbol 1Work, EnergyJouleJ 2PowerWattW 3ForceNewtonN 4ChargeCoulombC 5Magnetic fieldteslaT 6Magnetic Flux weberWb 7Electric FieldNewton / Coulomb N/C 9Dr Manjunatha S

SI Length Unit: Meter French Revolution Definition, Meter = XY/10,000,000 1 Meter = about 3.28 ft 1 km = 1000 m, 1 cm = 1/100 m, 1 mm = 1/1000 m Meter: 1 Meter is defined as the distance traveled by light in vacuum during a time of 1/299,792,458 second.

SI Time Unit: Second Second is defined in terms of an “atomic clock”– time taken for 9,192,631,770 oscillations of the light emitted by a 133 Cs atom. Defining units precisely is a science (important, for example, for GPS): –This clock will neither gain nor lose a second in 20 million years. 11Dr Manjunatha S

SI Mass Unit: Kilogram 1 Kilogram – the mass of a specific platinum-iridium alloy kept at International Bureau of Weights and Measures near Paris. (Seeking more accurate measure: Copies are kept in many other countries. Yao Ming is 141 kg, equivalent to weight of 141 pieces of the alloy cylinder. 12Dr Manjunatha S

13Dr Manjunatha S

Dimensional Analysis: The word dimension has a special meaning in physics. The dimension denotes the physical nature of a quantity. The expression which shows the fundamental quantity and power of unit is dimensional equation. The mass, length and time as M, L, and T are expressed in bracket [M a L b T c ]. 14Dr Manjunatha S

Dimensional formulae of physical quantities S. No.Physical QuantityPhysical FormulaSI Unit Dimensional formula 1AreaLength x Lengthm2m2 L X L= [M 0 L 2 T 0 ] 2VolumeL x b x t 3DensityMass/ volume 4Velocity 5Force 6Pressure 7Energy/Work 8Power 9Surface TenstionN/m 10Temperature 11 Gravitational Constant N m 2 /kg 2 12Volume/second 13Angular speedAngle/s [M 0 L 0 T -1 ] 14

Dimensional formulae of physical quantities S. No.Physical QuantityPhysical FormulaSI Unit Dimensional formula 1Electric Charge, QCurrent x timeCoulomb [M 0 L 0 T 1 A 1 ] 2Electric Potential, VWork/chargeVolt 3Resistance, RV/IOhm 4Sp. Resistance, ρRx area/l 5Electric field, EF/Q 6Capacity, CQ/VFarad 7Magnetic Induction, BF/Qv Sinθ tesla

Principle of homogeneity: The dimension of fundamental quantities of two sides of a physical relation must be same. [M a L b T c ] = [M x L y T z ] a=x, b=y, and c=z Dr Manjunatha S17

Types of variables and constants 1. Dimensional variables: Physical quantities which possess dimensions and have variables are called dimensional variables Ex: area, volume, speed, acceleration, force.. 2. Dimensionless variables: Quantities which have no dimension but have variables called dimensionless variables. Ex: angle, gravity, sinθ, cosθ... Dr Manjunatha S18

Types of variables and constants 3. Dimensional constants: Physical quantities which possess dimensions and have constant value are called dimensional constants. Ex: Planck’s constant, gravitational constant, speed of light 4. Dimensionless constants: Physical quantities which do not have dimension and have constant are called dimensionless constant. –Ex: π, e, pure no. Like 1,2,3,4,5,.. Dr Manjunatha S19

Conversion of Units The dimension equation can be used to one system into another system of unit. Dr Manjunatha S20

PROBLEMS: Example: 1 Joule is the unit of Work in SI system. Convert Joule into CGS system as erg. Work = [M 1 L 2 T -2 ]; a=1, b=2, c=-2 Dr Manjunatha S21

PROBLEMS... Example:2 Convert 10 Newton into dyne using dimensional analysis. Dr Manjunatha S22